[docs] Clean scheduler api (#4204)

* clean scheduler mixin

* up to dpmsolvermultistep

* finish cleaning

* first draft

* fix overview table

* apply feedback

* update reference code

docs/source/en/api/schedulers/score_sde_vp.md

@@ -10,15 +10,17 @@ an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express o
 specific language governing permissions and limitations under the License.
 -->
 
-# Variance Preserving Stochastic Differential Equation (VP-SDE) scheduler
+# ScoreSdeVpScheduler
 
-## Overview
+`ScoreSdeVpScheduler` is a variance preserving stochastic differential equation (SDE) scheduler.  It was introduced in the [Score-Based Generative Modeling through Stochastic Differential Equations](https://huggingface.co/papers/2011.13456) paper by Yang Song, Jascha Sohl-Dickstein, Diederik P. Kingma, Abhishek Kumar, Stefano Ermon, Ben Poole.
 
-Original paper can be found [here](https://arxiv.org/abs/2011.13456).
+The abstract from the paper is:
+
+*Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting noise, and a corresponding reverse-time SDE that transforms the prior distribution back into the data distribution by slowly removing the noise. Crucially, the reverse-time SDE depends only on the time-dependent gradient field (\aka, score) of the perturbed data distribution. By leveraging advances in score-based generative modeling, we can accurately estimate these scores with neural networks, and use numerical SDE solvers to generate samples. We show that this framework encapsulates previous approaches in score-based generative modeling and diffusion probabilistic modeling, allowing for new sampling procedures and new modeling capabilities. In particular, we introduce a predictor-corrector framework to correct errors in the evolution of the discretized reverse-time SDE. We also derive an equivalent neural ODE that samples from the same distribution as the SDE, but additionally enables exact likelihood computation, and improved sampling efficiency. In addition, we provide a new way to solve inverse problems with score-based models, as demonstrated with experiments on class-conditional generation, image inpainting, and colorization. Combined with multiple architectural improvements, we achieve record-breaking performance for unconditional image generation on CIFAR-10 with an Inception score of 9.89 and FID of 2.20, a competitive likelihood of 2.99 bits/dim, and demonstrate high fidelity generation of 1024 x 1024 images for the first time from a score-based generative model*.
 
 <Tip warning={true}>
 
-Score SDE-VP is under construction.
+🚧 This scheduler is under construction!
 
 </Tip>
 

docs/source/en/api/schedulers/singlestep_dpm_solver.md

@@ -10,11 +10,26 @@ an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express o
 specific language governing permissions and limitations under the License.
 -->
 
-# Singlestep DPM-Solver
+# DPMSolverSinglestepScheduler
 
-## Overview
+`DPMSolverSinglestepScheduler` is a single step scheduler from [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://huggingface.co/papers/2206.00927) and [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://huggingface.co/papers/2211.01095) by Cheng Lu, Yuhao Zhou, Fan Bao, Jianfei Chen, Chongxuan Li, and Jun Zhu.
 
-Original paper can be found [here](https://arxiv.org/abs/2206.00927) and the [improved version](https://arxiv.org/abs/2211.01095). The original implementation can be found [here](https://github.com/LuChengTHU/dpm-solver).
+DPMSolver (and the improved version DPMSolver++) is a fast dedicated high-order solver for diffusion ODEs with convergence order guarantee. Empirically, DPMSolver sampling with only 20 steps can generate high-quality
+samples, and it can generate quite good samples even in 10 steps.
+
+The original implementation can be found at [LuChengTHU/dpm-solver](https://github.com/LuChengTHU/dpm-solver).
+
+## Tips
+
+It is recommended to set `solver_order` to 2 for guide sampling, and `solver_order=3` for unconditional sampling.
+
+Dynamic thresholding from Imagen (https://huggingface.co/papers/2205.11487) is supported, and for pixel-space
+diffusion models, you can set both `algorithm_type="dpmsolver++"` and `thresholding=True` to use dynamic
+thresholding. This thresholding method is unsuitable for latent-space diffusion models such as
+Stable Diffusion.
 
 ## DPMSolverSinglestepScheduler
-[[autodoc]] DPMSolverSinglestepScheduler
+[[autodoc]] DPMSolverSinglestepScheduler
\ No newline at end of file
+
+## SchedulerOutput
+[[autodoc]] schedulers.scheduling_utils.SchedulerOutput
\ No newline at end of file

docs/source/en/api/schedulers/stochastic_karras_ve.md

@@ -10,11 +10,12 @@ an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express o
 specific language governing permissions and limitations under the License.
 -->
 
-# Variance exploding, stochastic sampling from Karras et. al
+# KarrasVeScheduler
 
-## Overview
-
-Original paper can be found [here](https://arxiv.org/abs/2206.00364).
+`KarrasVeScheduler` is a stochastic sampler tailored o variance-expanding (VE) models. It is based on the [Elucidating the Design Space of Diffusion-Based Generative Models](https://huggingface.co/papers/2206.00364) and [Score-based generative modeling through stochastic differential equations](https://huggingface.co/papers/2011.13456) papers.
 
 ## KarrasVeScheduler
-[[autodoc]] KarrasVeScheduler
+[[autodoc]] KarrasVeScheduler
\ No newline at end of file
+
+## KarrasVeOutput
+[[autodoc]] schedulers.scheduling_karras_ve.KarrasVeOutput
\ No newline at end of file

docs/source/en/api/schedulers/unipc.md

@@ -10,15 +10,28 @@ an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express o
 specific language governing permissions and limitations under the License.
 -->
 
-# UniPC
+# UniPCMultistepScheduler
 
-## Overview
+`UniPCMultistepScheduler` is a training-free framework designed for fast sampling of diffusion models. It was introduced in [UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models](https://huggingface.co/papers/2302.04867) by Wenliang Zhao, Lujia Bai, Yongming Rao, Jie Zhou, Jiwen Lu.
 
-UniPC is a training-free framework designed for the fast sampling of diffusion models, which consists of a corrector (UniC) and a predictor (UniP) that share a unified analytical form and support arbitrary orders.
+It consists of a corrector (UniC) and a predictor (UniP) that share a unified analytical form and support arbitrary orders.
+UniPC is by design model-agnostic, supporting pixel-space/latent-space DPMs on unconditional/conditional sampling. It can also be applied to both noise prediction and data prediction models. The corrector UniC can be also applied after any off-the-shelf solvers to increase the order of accuracy.
 
-For more details about the method, please refer to the [paper](https://arxiv.org/abs/2302.04867) and the [code](https://github.com/wl-zhao/UniPC).
+The abstract from the paper is:
 
-Fast Sampling of Diffusion Models with Exponential Integrator.
+*Diffusion probabilistic models (DPMs) have demonstrated a very promising ability in high-resolution image synthesis. However, sampling from a pre-trained DPM usually requires hundreds of model evaluations, which is computationally expensive. Despite recent progress in designing high-order solvers for DPMs, there still exists room for further speedup, especially in extremely few steps (e.g., 5~10 steps). Inspired by the predictor-corrector for ODE solvers, we develop a unified corrector (UniC) that can be applied after any existing DPM sampler to increase the order of accuracy without extra model evaluations, and derive a unified predictor (UniP) that supports arbitrary order as a byproduct. Combining UniP and UniC, we propose a unified predictor-corrector framework called UniPC for the fast sampling of DPMs, which has a unified analytical form for any order and can significantly improve the sampling quality over previous methods. We evaluate our methods through extensive experiments including both unconditional and conditional sampling using pixel-space and latent-space DPMs. Our UniPC can achieve 3.87 FID on CIFAR10 (unconditional) and 7.51 FID on ImageNet 256times256 (conditional) with only 10 function evaluations. Code is available at https://github.com/wl-zhao/UniPC*.
+
+The original codebase can be found at [wl-zhao/UniPC](https://github.com/wl-zhao/UniPC).
+
+## Tips
+
+It is recommended to set `solver_order` to 2 for guide sampling, and `solver_order=3` for unconditional sampling.
+
+Dynamic thresholding from Imagen (https://huggingface.co/papers/2205.11487) is supported, and for pixel-space
+diffusion models, you can set both `predict_x0=True` and `thresholding=True` to use dynamic thresholding. This thresholding method is unsuitable for latent-space diffusion models such as Stable Diffusion.
 
 ## UniPCMultistepScheduler
 [[autodoc]] UniPCMultistepScheduler
+
+## SchedulerOutput
+[[autodoc]] schedulers.scheduling_utils.SchedulerOutput
\ No newline at end of file

docs/source/en/api/schedulers/vq_diffusion.md

@@ -12,9 +12,14 @@ specific language governing permissions and limitations under the License.
 
 # VQDiffusionScheduler
 
-## Overview
+`VQDiffusionScheduler` converts the transformer model's output into a sample for the unnoised image at the previous diffusion timestep. It was introduced in [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://huggingface.co/papers/2111.14822) by Shuyang Gu, Dong Chen, Jianmin Bao, Fang Wen, Bo Zhang, Dongdong Chen, Lu Yuan, Baining Guo.
 
-Original paper can be found [here](https://arxiv.org/abs/2111.14822)
+The abstract from the paper is:
+
+*We present the vector quantized diffusion (VQ-Diffusion) model for text-to-image generation. This method is based on a vector quantized variational autoencoder (VQ-VAE) whose latent space is modeled by a conditional variant of the recently developed Denoising Diffusion Probabilistic Model (DDPM). We find that this latent-space method is well-suited for text-to-image generation tasks because it not only eliminates the unidirectional bias with existing methods but also allows us to incorporate a mask-and-replace diffusion strategy to avoid the accumulation of errors, which is a serious problem with existing methods. Our experiments show that the VQ-Diffusion produces significantly better text-to-image generation results when compared with conventional autoregressive (AR) models with similar numbers of parameters. Compared with previous GAN-based text-to-image methods, our VQ-Diffusion can handle more complex scenes and improve the synthesized image quality by a large margin. Finally, we show that the image generation computation in our method can be made highly efficient by reparameterization. With traditional AR methods, the text-to-image generation time increases linearly with the output image resolution and hence is quite time consuming even for normal size images. The VQ-Diffusion allows us to achieve a better trade-off between quality and speed. Our experiments indicate that the VQ-Diffusion model with the reparameterization is fifteen times faster than traditional AR methods while achieving a better image quality.*
 
 ## VQDiffusionScheduler
-[[autodoc]] VQDiffusionScheduler
+[[autodoc]] VQDiffusionScheduler
\ No newline at end of file
+
+## VQDiffusionSchedulerOutput
+[[autodoc]] schedulers.scheduling_vq_diffusion.VQDiffusionSchedulerOutput
\ No newline at end of file

src/diffusers/schedulers/scheduling_consistency_models.py

@@ -29,11 +29,11 @@ logger = logging.get_logger(__name__)  # pylint: disable=invalid-name
 @dataclass
 class CMStochasticIterativeSchedulerOutput(BaseOutput):
     """
-    Output class for the scheduler's step function output.
+    Output class for the scheduler's `step` function.
 
     Args:
         prev_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
-            Computed sample (x_{t-1}) of previous timestep. `prev_sample` should be used as next model input in the
+            Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the
             denoising loop.
     """
 
@@ -42,38 +42,32 @@ class CMStochasticIterativeSchedulerOutput(BaseOutput):
 
 class CMStochasticIterativeScheduler(SchedulerMixin, ConfigMixin):
     """
-    Multistep and onestep sampling for consistency models from Song et al. 2023 [1]. This implements Algorithm 1 in the
-    paper [1].
+    Multistep and onestep sampling for consistency models.
 
-    [1] Song, Yang and Dhariwal, Prafulla and Chen, Mark and Sutskever, Ilya. "Consistency Models"
-    https://arxiv.org/pdf/2303.01469 [2] Karras, Tero, et al. "Elucidating the Design Space of Diffusion-Based
-    Generative Models." https://arxiv.org/abs/2206.00364
-
-    [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
-    function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`.
-    [`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and
-    [`~SchedulerMixin.from_pretrained`] functions.
+    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
+    methods the library implements for all schedulers such as loading and saving.
 
     Args:
-        num_train_timesteps (`int`): number of diffusion steps used to train the model.
-        sigma_min (`float`):
-            Minimum noise magnitude in the sigma schedule. This was set to 0.002 in the original implementation.
-        sigma_max (`float`):
-            Maximum noise magnitude in the sigma schedule. This was set to 80.0 in the original implementation.
-        sigma_data (`float`):
-            The standard deviation of the data distribution, following the EDM paper [2]. This was set to 0.5 in the
-            original implementation, which is also the original value suggested in the EDM paper.
-        s_noise (`float`):
+        num_train_timesteps (`int`, defaults to 40):
+            The number of diffusion steps to train the model.
+        sigma_min (`float`, defaults to 0.002):
+            Minimum noise magnitude in the sigma schedule. Defaults to 0.002 from the original implementation.
+        sigma_max (`float`, defaults to 80.0):
+            Maximum noise magnitude in the sigma schedule. Defaults to 80.0 from the original implementation.
+        sigma_data (`float`, defaults to 0.5):
+            The standard deviation of the data distribution from the EDM
+            [paper](https://huggingface.co/papers/2206.00364). Defaults to 0.5 from the original implementation.
+        s_noise (`float`, defaults to 1.0):
             The amount of additional noise to counteract loss of detail during sampling. A reasonable range is [1.000,
-            1.011]. This was set to 1.0 in the original implementation.
-        rho (`float`):
-            The rho parameter used for calculating the Karras sigma schedule, introduced in the EDM paper [2]. This was
-            set to 7.0 in the original implementation, which is also the original value suggested in the EDM paper.
-        clip_denoised (`bool`):
-            Whether to clip the denoised outputs to `(-1, 1)`. Defaults to `True`.
+            1.011]. Defaults to 1.0 from the original implementation.
+        rho (`float`, defaults to 7.0):
+            The parameter for calculating the Karras sigma schedule from the EDM
+            [paper](https://huggingface.co/papers/2206.00364). Defaults to 7.0 from the original implementation.
+        clip_denoised (`bool`, defaults to `True`):
+            Whether to clip the denoised outputs to `(-1, 1)`.
         timesteps (`List` or `np.ndarray` or `torch.Tensor`, *optional*):
-            Optionally, an explicit timestep schedule can be specified. The timesteps are expected to be in increasing
-            order.
+            An explicit timestep schedule that can be optionally specified. The timesteps are expected to be in
+            increasing order.
     """
 
     order = 1
@@ -114,13 +108,17 @@ class CMStochasticIterativeScheduler(SchedulerMixin, ConfigMixin):
         self, sample: torch.FloatTensor, timestep: Union[float, torch.FloatTensor]
     ) -> torch.FloatTensor:
         """
-        Scales the consistency model input by `(sigma**2 + sigma_data**2) ** 0.5`, following the EDM model.
+        Scales the consistency model input by `(sigma**2 + sigma_data**2) ** 0.5`.
 
         Args:
-            sample (`torch.FloatTensor`): input sample
-            timestep (`float` or `torch.FloatTensor`): the current timestep in the diffusion chain
+            sample (`torch.FloatTensor`):
+                The input sample.
+            timestep (`float` or `torch.FloatTensor`):
+                The current timestep in the diffusion chain.
+
         Returns:
-            `torch.FloatTensor`: scaled input sample
+            `torch.FloatTensor`:
+                A scaled input sample.
         """
         # Get sigma corresponding to timestep
         if isinstance(timestep, torch.Tensor):
@@ -135,12 +133,15 @@ class CMStochasticIterativeScheduler(SchedulerMixin, ConfigMixin):
 
     def sigma_to_t(self, sigmas: Union[float, np.ndarray]):
         """
-        Gets scaled timesteps from the Karras sigmas, for input to the consistency model.
+        Gets scaled timesteps from the Karras sigmas for input to the consistency model.
 
         Args:
-            sigmas (`float` or `np.ndarray`): single Karras sigma or array of Karras sigmas
+            sigmas (`float` or `np.ndarray`):
+                A single Karras sigma or an array of Karras sigmas.
+
         Returns:
-            `float` or `np.ndarray`: scaled input timestep or scaled input timestep array
+            `float` or `np.ndarray`:
+                A scaled input timestep or scaled input timestep array.
         """
         if not isinstance(sigmas, np.ndarray):
             sigmas = np.array(sigmas, dtype=np.float64)
@@ -156,17 +157,17 @@ class CMStochasticIterativeScheduler(SchedulerMixin, ConfigMixin):
         timesteps: Optional[List[int]] = None,
     ):
         """
-        Sets the timesteps used for the diffusion chain. Supporting function to be run before inference.
+        Sets the timesteps used for the diffusion chain (to be run before inference).
 
         Args:
             num_inference_steps (`int`):
-                the number of diffusion steps used when generating samples with a pre-trained model.
-            device (`str` or `torch.device`, optional):
-                the device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
-            timesteps (`List[int]`, optional):
-                custom timesteps used to support arbitrary spacing between timesteps. If `None`, then the default
-                timestep spacing strategy of equal spacing between timesteps is used. If passed, `num_inference_steps`
-                must be `None`.
+                The number of diffusion steps used when generating samples with a pre-trained model.
+            device (`str` or `torch.device`, *optional*):
+                The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
+            timesteps (`List[int]`, *optional*):
+                Custom timesteps used to support arbitrary spacing between timesteps. If `None`, then the default
+                timestep spacing strategy of equal spacing between timesteps is used. If `timesteps` is passed,
+                `num_inference_steps` must be `None`.
         """
         if num_inference_steps is None and timesteps is None:
             raise ValueError("Exactly one of `num_inference_steps` or `timesteps` must be supplied.")
@@ -241,17 +242,22 @@ class CMStochasticIterativeScheduler(SchedulerMixin, ConfigMixin):
 
     def get_scalings_for_boundary_condition(self, sigma):
         """
-        Gets the scalings used in the consistency model parameterization, following Appendix C of the original paper.
-        This enforces the consistency model boundary condition.
+        Gets the scalings used in the consistency model parameterization (from Appendix C of the
+        [paper](https://huggingface.co/papers/2303.01469)) to enforce boundary condition.
 
-        Note that `epsilon` in the equations for c_skip and c_out is set to sigma_min.
+        <Tip>
+
+        `epsilon` in the equations for `c_skip` and `c_out` is set to `sigma_min`.
+
+        </Tip>
 
         Args:
             sigma (`torch.FloatTensor`):
                 The current sigma in the Karras sigma schedule.
+
         Returns:
             `tuple`:
-                A two-element tuple where c_skip (which weights the current sample) is the first element and c_out
+                A two-element tuple where `c_skip` (which weights the current sample) is the first element and `c_out`
                 (which weights the consistency model output) is the second element.
         """
         sigma_min = self.config.sigma_min
@@ -270,20 +276,27 @@ class CMStochasticIterativeScheduler(SchedulerMixin, ConfigMixin):
         return_dict: bool = True,
     ) -> Union[CMStochasticIterativeSchedulerOutput, Tuple]:
         """
-        Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
+        Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
         process from the learned model outputs (most often the predicted noise).
 
         Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`float`): current timestep in the diffusion chain.
+            model_output (`torch.FloatTensor`):
+                The direct output from the learned diffusion model.
+            timestep (`float`):
+                The current timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
-            generator (`torch.Generator`, *optional*): Random number generator.
-            return_dict (`bool`): option for returning tuple rather than EulerDiscreteSchedulerOutput class
+                A current instance of a sample created by the diffusion process.
+            generator (`torch.Generator`, *optional*):
+                A random number generator.
+            return_dict (`bool`, *optional*, defaults to `True`):
+                Whether or not to return a
+                [`~schedulers.scheduling_consistency_models.CMStochasticIterativeSchedulerOutput`] or `tuple`.
+
         Returns:
-            [`~schedulers.scheduling_utils.CMStochasticIterativeSchedulerOutput`] or `tuple`:
-            [`~schedulers.scheduling_utils.CMStochasticIterativeSchedulerOutput`] if `return_dict` is True, otherwise a
-            `tuple`. When returning a tuple, the first element is the sample tensor.
+            [`~schedulers.scheduling_consistency_models.CMStochasticIterativeSchedulerOutput`] or `tuple`:
+                If return_dict is `True`,
+                [`~schedulers.scheduling_consistency_models.CMStochasticIterativeSchedulerOutput`] is returned,
+                otherwise a tuple is returned where the first element is the sample tensor.
         """
 
         if (

src/diffusers/schedulers/scheduling_ddim.py

@@ -31,14 +31,14 @@ from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin
 # Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->DDIM
 class DDIMSchedulerOutput(BaseOutput):
     """
-    Output class for the scheduler's step function output.
+    Output class for the scheduler's `step` function output.
 
     Args:
         prev_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
-            Computed sample (x_{t-1}) of previous timestep. `prev_sample` should be used as next model input in the
+            Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the
             denoising loop.
         pred_original_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
-            The predicted denoised sample (x_{0}) based on the model output from the current timestep.
+            The predicted denoised sample `(x_{0})` based on the model output from the current timestep.
             `pred_original_sample` can be used to preview progress or for guidance.
     """
 
@@ -129,57 +129,53 @@ def rescale_zero_terminal_snr(betas):
 
 class DDIMScheduler(SchedulerMixin, ConfigMixin):
     """
-    Denoising diffusion implicit models is a scheduler that extends the denoising procedure introduced in denoising
-    diffusion probabilistic models (DDPMs) with non-Markovian guidance.
+    `DDIMScheduler` extends the denoising procedure introduced in denoising diffusion probabilistic models (DDPMs) with
+    non-Markovian guidance.
 
-    [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
-    function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`.
-    [`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and
-    [`~SchedulerMixin.from_pretrained`] functions.
-
-    For more details, see the original paper: https://arxiv.org/abs/2010.02502
+    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
+    methods the library implements for all schedulers such as loading and saving.
 
     Args:
-        num_train_timesteps (`int`): number of diffusion steps used to train the model.
-        beta_start (`float`): the starting `beta` value of inference.
-        beta_end (`float`): the final `beta` value.
-        beta_schedule (`str`):
-            the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
+        num_train_timesteps (`int`, defaults to 1000):
+            The number of diffusion steps to train the model.
+        beta_start (`float`, defaults to 0.0001):
+            The starting `beta` value of inference.
+        beta_end (`float`, defaults to 0.02):
+            The final `beta` value.
+        beta_schedule (`str`, defaults to `"linear"`):
+            The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
             `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
-        trained_betas (`np.ndarray`, optional):
-            option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
-        clip_sample (`bool`, default `True`):
-            option to clip predicted sample for numerical stability.
-        clip_sample_range (`float`, default `1.0`):
-            the maximum magnitude for sample clipping. Valid only when `clip_sample=True`.
-        set_alpha_to_one (`bool`, default `True`):
-            each diffusion step uses the value of alphas product at that step and at the previous one. For the final
-            step there is no previous alpha. When this option is `True` the previous alpha product is fixed to `1`,
-            otherwise it uses the value of alpha at step 0.
-        steps_offset (`int`, default `0`):
-            an offset added to the inference steps. You can use a combination of `offset=1` and
-            `set_alpha_to_one=False`, to make the last step use step 0 for the previous alpha product, as done in
-            stable diffusion.
-        prediction_type (`str`, default `epsilon`, optional):
-            prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion
-            process), `sample` (directly predicting the noisy sample`) or `v_prediction` (see section 2.4
-            https://imagen.research.google/video/paper.pdf)
-        thresholding (`bool`, default `False`):
-            whether to use the "dynamic thresholding" method (introduced by Imagen, https://arxiv.org/abs/2205.11487).
-            Note that the thresholding method is unsuitable for latent-space diffusion models (such as
-            stable-diffusion).
-        dynamic_thresholding_ratio (`float`, default `0.995`):
-            the ratio for the dynamic thresholding method. Default is `0.995`, the same as Imagen
-            (https://arxiv.org/abs/2205.11487). Valid only when `thresholding=True`.
-        sample_max_value (`float`, default `1.0`):
-            the threshold value for dynamic thresholding. Valid only when `thresholding=True`.
-        timestep_spacing (`str`, default `"leading"`):
-            The way the timesteps should be scaled. Refer to Table 2. of [Common Diffusion Noise Schedules and Sample
-            Steps are Flawed](https://arxiv.org/abs/2305.08891) for more information.
-        rescale_betas_zero_snr (`bool`, default `False`):
-            whether to rescale the betas to have zero terminal SNR (proposed by https://arxiv.org/pdf/2305.08891.pdf).
-            This can enable the model to generate very bright and dark samples instead of limiting it to samples with
-            medium brightness. Loosely related to
+        trained_betas (`np.ndarray`, *optional*):
+            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
+        clip_sample (`bool`, defaults to `True`):
+            Clip the predicted sample for numerical stability.
+        clip_sample_range (`float`, defaults to 1.0):
+            The maximum magnitude for sample clipping. Valid only when `clip_sample=True`.
+        set_alpha_to_one (`bool`, defaults to `True`):
+            Each diffusion step uses the alphas product value at that step and at the previous one. For the final step
+            there is no previous alpha. When this option is `True` the previous alpha product is fixed to `1`,
+            otherwise it uses the alpha value at step 0.
+        steps_offset (`int`, defaults to 0):
+            An offset added to the inference steps. You can use a combination of `offset=1` and
+            `set_alpha_to_one=False` to make the last step use step 0 for the previous alpha product like in Stable
+            Diffusion.
+        prediction_type (`str`, defaults to `epsilon`, *optional*):
+            Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
+            `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen
+            Video](https://imagen.research.google/video/paper.pdf) paper).
+        thresholding (`bool`, defaults to `False`):
+            Whether to use the "dynamic thresholding" method. This is unsuitable for latent-space diffusion models such
+            as Stable Diffusion.
+        dynamic_thresholding_ratio (`float`, defaults to 0.995):
+            The ratio for the dynamic thresholding method. Valid only when `thresholding=True`.
+        sample_max_value (`float`, defaults to 1.0):
+            The threshold value for dynamic thresholding. Valid only when `thresholding=True`.
+        timestep_spacing (`str`, defaults to `"leading"`):
+            The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
+            Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
+        rescale_betas_zero_snr (`bool`, defaults to `False`):
+            Whether to rescale the betas to have zero terminal SNR. This enables the model to generate very bright and
+            dark samples instead of limiting it to samples with medium brightness. Loosely related to
             [`--offset_noise`](https://github.com/huggingface/diffusers/blob/74fd735eb073eb1d774b1ab4154a0876eb82f055/examples/dreambooth/train_dreambooth.py#L506).
     """
 
@@ -246,11 +242,14 @@ class DDIMScheduler(SchedulerMixin, ConfigMixin):
         current timestep.
 
         Args:
-            sample (`torch.FloatTensor`): input sample
-            timestep (`int`, optional): current timestep
+            sample (`torch.FloatTensor`):
+                The input sample.
+            timestep (`int`, *optional*):
+                The current timestep in the diffusion chain.
 
         Returns:
-            `torch.FloatTensor`: scaled input sample
+            `torch.FloatTensor`:
+                A scaled input sample.
         """
         return sample
 
@@ -301,11 +300,11 @@ class DDIMScheduler(SchedulerMixin, ConfigMixin):
 
     def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
         """
-        Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.
+        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
 
         Args:
             num_inference_steps (`int`):
-                the number of diffusion steps used when generating samples with a pre-trained model.
+                The number of diffusion steps used when generating samples with a pre-trained model.
         """
 
         if num_inference_steps > self.config.num_train_timesteps:
@@ -356,29 +355,35 @@ class DDIMScheduler(SchedulerMixin, ConfigMixin):
         return_dict: bool = True,
     ) -> Union[DDIMSchedulerOutput, Tuple]:
         """
-        Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
+        Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
         process from the learned model outputs (most often the predicted noise).
 
         Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`int`): current discrete timestep in the diffusion chain.
+            model_output (`torch.FloatTensor`):
+                The direct output from learned diffusion model.
+            timestep (`float`):
+                The current discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
-            eta (`float`): weight of noise for added noise in diffusion step.
-            use_clipped_model_output (`bool`): if `True`, compute "corrected" `model_output` from the clipped
-                predicted original sample. Necessary because predicted original sample is clipped to [-1, 1] when
-                `self.config.clip_sample` is `True`. If no clipping has happened, "corrected" `model_output` would
-                coincide with the one provided as input and `use_clipped_model_output` will have not effect.
-            generator: random number generator.
-            variance_noise (`torch.FloatTensor`): instead of generating noise for the variance using `generator`, we
-                can directly provide the noise for the variance itself. This is useful for methods such as
-                CycleDiffusion. (https://arxiv.org/abs/2210.05559)
-            return_dict (`bool`): option for returning tuple rather than DDIMSchedulerOutput class
+                A current instance of a sample created by the diffusion process.
+            eta (`float`):
+                The weight of noise for added noise in diffusion step.
+            use_clipped_model_output (`bool`, defaults to `False`):
+                If `True`, computes "corrected" `model_output` from the clipped predicted original sample. Necessary
+                because predicted original sample is clipped to [-1, 1] when `self.config.clip_sample` is `True`. If no
+                clipping has happened, "corrected" `model_output` would coincide with the one provided as input and
+                `use_clipped_model_output` has no effect.
+            generator (`torch.Generator`, *optional*):
+                A random number generator.
+            variance_noise (`torch.FloatTensor`):
+                Alternative to generating noise with `generator` by directly providing the noise for the variance
+                itself. Useful for methods such as [`CycleDiffusion`].
+            return_dict (`bool`, *optional*, defaults to `True`):
+                Whether or not to return a [`~schedulers.scheduling_ddim.DDIMSchedulerOutput`] or `tuple`.
 
         Returns:
             [`~schedulers.scheduling_utils.DDIMSchedulerOutput`] or `tuple`:
-            [`~schedulers.scheduling_utils.DDIMSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When
-            returning a tuple, the first element is the sample tensor.
+                If return_dict is `True`, [`~schedulers.scheduling_ddim.DDIMSchedulerOutput`] is returned, otherwise a
+                tuple is returned where the first element is the sample tensor.
 
         """
         if self.num_inference_steps is None:

src/diffusers/schedulers/scheduling_ddim_inverse.py

@@ -30,14 +30,14 @@ from diffusers.utils import BaseOutput, deprecate
 # Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->DDIM
 class DDIMSchedulerOutput(BaseOutput):
     """
-    Output class for the scheduler's step function output.
+    Output class for the scheduler's `step` function output.
 
     Args:
         prev_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
-            Computed sample (x_{t-1}) of previous timestep. `prev_sample` should be used as next model input in the
+            Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the
             denoising loop.
         pred_original_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
-            The predicted denoised sample (x_{0}) based on the model output from the current timestep.
+            The predicted denoised sample `(x_{0})` based on the model output from the current timestep.
             `pred_original_sample` can be used to preview progress or for guidance.
     """
 
@@ -129,47 +129,45 @@ def rescale_zero_terminal_snr(betas):
 
 class DDIMInverseScheduler(SchedulerMixin, ConfigMixin):
     """
-    DDIMInverseScheduler is the reverse scheduler of [`DDIMScheduler`].
+    `DDIMInverseScheduler` is the reverse scheduler of [`DDIMScheduler`].
 
-    [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
-    function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`.
-    [`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and
-    [`~SchedulerMixin.from_pretrained`] functions.
-
-    For more details, see the original paper: https://arxiv.org/abs/2010.02502
+    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
+    methods the library implements for all schedulers such as loading and saving.
 
     Args:
-        num_train_timesteps (`int`): number of diffusion steps used to train the model.
-        beta_start (`float`): the starting `beta` value of inference.
-        beta_end (`float`): the final `beta` value.
-        beta_schedule (`str`):
-            the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
+        num_train_timesteps (`int`, defaults to 1000):
+            The number of diffusion steps to train the model.
+        beta_start (`float`, defaults to 0.0001):
+            The starting `beta` value of inference.
+        beta_end (`float`, defaults to 0.02):
+            The final `beta` value.
+        beta_schedule (`str`, defaults to `"linear"`):
+            The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
             `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
-        trained_betas (`np.ndarray`, optional):
-            option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
-        clip_sample (`bool`, default `True`):
-            option to clip predicted sample for numerical stability.
-        clip_sample_range (`float`, default `1.0`):
-            the maximum magnitude for sample clipping. Valid only when `clip_sample=True`.
-        set_alpha_to_zero (`bool`, default `True`):
-            each diffusion step uses the value of alphas product at that step and at the previous one. For the final
-            step there is no previous alpha. When this option is `True` the previous alpha product is fixed to `0`,
-            otherwise it uses the value of alpha at step `num_train_timesteps - 1`.
-        steps_offset (`int`, default `0`):
-            an offset added to the inference steps. You can use a combination of `offset=1` and
-            `set_alpha_to_zero=False`, to make the last step use step `num_train_timesteps - 1` for the previous alpha
+        trained_betas (`np.ndarray`, *optional*):
+            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
+        clip_sample (`bool`, defaults to `True`):
+            Clip the predicted sample for numerical stability.
+        clip_sample_range (`float`, defaults to 1.0):
+            The maximum magnitude for sample clipping. Valid only when `clip_sample=True`.
+        set_alpha_to_one (`bool`, defaults to `True`):
+            Each diffusion step uses the alphas product value at that step and at the previous one. For the final step
+            there is no previous alpha. When this option is `True` the previous alpha product is fixed to 0, otherwise
+            it uses the alpha value at step `num_train_timesteps - 1`.
+        steps_offset (`int`, defaults to 0):
+            An offset added to the inference steps. You can use a combination of `offset=1` and
+            `set_alpha_to_one=False` to make the last step use `num_train_timesteps - 1` for the previous alpha
             product.
-        prediction_type (`str`, default `epsilon`, optional):
-            prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion
-            process), `sample` (directly predicting the noisy sample`) or `v_prediction` (see section 2.4
-            https://imagen.research.google/video/paper.pdf)
-        timestep_spacing (`str`, default `"leading"`):
-            The way the timesteps should be scaled. Refer to Table 2. of [Common Diffusion Noise Schedules and Sample
-            Steps are Flawed](https://arxiv.org/abs/2305.08891) for more information.
-        rescale_betas_zero_snr (`bool`, default `False`):
-            whether to rescale the betas to have zero terminal SNR (proposed by https://arxiv.org/pdf/2305.08891.pdf).
-            This can enable the model to generate very bright and dark samples instead of limiting it to samples with
-            medium brightness. Loosely related to
+        prediction_type (`str`, defaults to `epsilon`, *optional*):
+            Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
+            `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen
+            Video](https://imagen.research.google/video/paper.pdf) paper).
+        timestep_spacing (`str`, defaults to `"leading"`):
+            The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
+            Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
+        rescale_betas_zero_snr (`bool`, defaults to `False`):
+            Whether to rescale the betas to have zero terminal SNR. This enables the model to generate very bright and
+            dark samples instead of limiting it to samples with medium brightness. Loosely related to
             [`--offset_noise`](https://github.com/huggingface/diffusers/blob/74fd735eb073eb1d774b1ab4154a0876eb82f055/examples/dreambooth/train_dreambooth.py#L506).
     """
 
@@ -243,21 +241,24 @@ class DDIMInverseScheduler(SchedulerMixin, ConfigMixin):
         current timestep.
 
         Args:
-            sample (`torch.FloatTensor`): input sample
-            timestep (`int`, optional): current timestep
+            sample (`torch.FloatTensor`):
+                The input sample.
+            timestep (`int`, *optional*):
+                The current timestep in the diffusion chain.
 
         Returns:
-            `torch.FloatTensor`: scaled input sample
+            `torch.FloatTensor`:
+                A scaled input sample.
         """
         return sample
 
     def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
         """
-        Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.
+        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
 
         Args:
             num_inference_steps (`int`):
-                the number of diffusion steps used when generating samples with a pre-trained model.
+                The number of diffusion steps used when generating samples with a pre-trained model.
         """
 
         if num_inference_steps > self.config.num_train_timesteps:
@@ -302,6 +303,37 @@ class DDIMInverseScheduler(SchedulerMixin, ConfigMixin):
         variance_noise: Optional[torch.FloatTensor] = None,
         return_dict: bool = True,
     ) -> Union[DDIMSchedulerOutput, Tuple]:
+        """
+        Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
+        process from the learned model outputs (most often the predicted noise).
+
+        Args:
+            model_output (`torch.FloatTensor`):
+                The direct output from learned diffusion model.
+            timestep (`float`):
+                The current discrete timestep in the diffusion chain.
+            sample (`torch.FloatTensor`):
+                A current instance of a sample created by the diffusion process.
+            eta (`float`):
+                The weight of noise for added noise in diffusion step.
+            use_clipped_model_output (`bool`, defaults to `False`):
+                If `True`, computes "corrected" `model_output` from the clipped predicted original sample. Necessary
+                because predicted original sample is clipped to [-1, 1] when `self.config.clip_sample` is `True`. If no
+                clipping has happened, "corrected" `model_output` would coincide with the one provided as input and
+                `use_clipped_model_output` has no effect.
+            variance_noise (`torch.FloatTensor`):
+                Alternative to generating noise with `generator` by directly providing the noise for the variance
+                itself. Useful for methods such as [`CycleDiffusion`].
+            return_dict (`bool`, *optional*, defaults to `True`):
+                Whether or not to return a [`~schedulers.scheduling_ddim_inverse.DDIMInverseSchedulerOutput`] or
+                `tuple`.
+
+        Returns:
+            [`~schedulers.scheduling_ddim_inverse.DDIMInverseSchedulerOutput`] or `tuple`:
+                If return_dict is `True`, [`~schedulers.scheduling_ddim_inverse.DDIMInverseSchedulerOutput`] is
+                returned, otherwise a tuple is returned where the first element is the sample tensor.
+
+        """
         # 1. get previous step value (=t+1)
         prev_timestep = timestep + self.config.num_train_timesteps // self.num_inference_steps
 

src/diffusers/schedulers/scheduling_ddim_parallel.py

@@ -31,14 +31,14 @@ from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin
 # Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput
 class DDIMParallelSchedulerOutput(BaseOutput):
     """
-    Output class for the scheduler's step function output.
+    Output class for the scheduler's `step` function output.
 
     Args:
         prev_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
-            Computed sample (x_{t-1}) of previous timestep. `prev_sample` should be used as next model input in the
+            Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the
             denoising loop.
         pred_original_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
-            The predicted denoised sample (x_{0}) based on the model output from the current timestep.
+            The predicted denoised sample `(x_{0})` based on the model output from the current timestep.
             `pred_original_sample` can be used to preview progress or for guidance.
     """
 
@@ -250,11 +250,14 @@ class DDIMParallelScheduler(SchedulerMixin, ConfigMixin):
         current timestep.
 
         Args:
-            sample (`torch.FloatTensor`): input sample
-            timestep (`int`, optional): current timestep
+            sample (`torch.FloatTensor`):
+                The input sample.
+            timestep (`int`, *optional*):
+                The current timestep in the diffusion chain.
 
         Returns:
-            `torch.FloatTensor`: scaled input sample
+            `torch.FloatTensor`:
+                A scaled input sample.
         """
         return sample
 
@@ -320,11 +323,11 @@ class DDIMParallelScheduler(SchedulerMixin, ConfigMixin):
     # Copied from diffusers.schedulers.scheduling_ddim.DDIMScheduler.set_timesteps
     def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
         """
-        Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.
+        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
 
         Args:
             num_inference_steps (`int`):
-                the number of diffusion steps used when generating samples with a pre-trained model.
+                The number of diffusion steps used when generating samples with a pre-trained model.
         """
 
         if num_inference_steps > self.config.num_train_timesteps:

src/diffusers/schedulers/scheduling_ddpm.py

@@ -29,14 +29,14 @@ from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin
 @dataclass
 class DDPMSchedulerOutput(BaseOutput):
     """
-    Output class for the scheduler's step function output.
+    Output class for the scheduler's `step` function output.
 
     Args:
         prev_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
-            Computed sample (x_{t-1}) of previous timestep. `prev_sample` should be used as next model input in the
+            Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the
             denoising loop.
         pred_original_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
-            The predicted denoised sample (x_{0}) based on the model output from the current timestep.
+            The predicted denoised sample `(x_{0})` based on the model output from the current timestep.
             `pred_original_sample` can be used to preview progress or for guidance.
     """
 
@@ -90,52 +90,46 @@ def betas_for_alpha_bar(
 
 class DDPMScheduler(SchedulerMixin, ConfigMixin):
     """
-    Denoising diffusion probabilistic models (DDPMs) explores the connections between denoising score matching and
-    Langevin dynamics sampling.
+    `DDPMScheduler` explores the connections between denoising score matching and Langevin dynamics sampling.
 
-    [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
-    function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`.
-    [`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and
-    [`~SchedulerMixin.from_pretrained`] functions.
-
-    For more details, see the original paper: https://arxiv.org/abs/2006.11239
+    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
+    methods the library implements for all schedulers such as loading and saving.
 
     Args:
-        num_train_timesteps (`int`): number of diffusion steps used to train the model.
-        beta_start (`float`): the starting `beta` value of inference.
-        beta_end (`float`): the final `beta` value.
-        beta_schedule (`str`):
-            the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
-            `linear`, `scaled_linear`, `squaredcos_cap_v2` or `sigmoid`.
-        trained_betas (`np.ndarray`, optional):
-            option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
-        variance_type (`str`):
-            options to clip the variance used when adding noise to the denoised sample. Choose from `fixed_small`,
-            `fixed_small_log`, `fixed_large`, `fixed_large_log`, `learned` or `learned_range`.
-        clip_sample (`bool`, default `True`):
-            option to clip predicted sample for numerical stability.
-        clip_sample_range (`float`, default `1.0`):
-            the maximum magnitude for sample clipping. Valid only when `clip_sample=True`.
-        prediction_type (`str`, default `epsilon`, optional):
-            prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion
-            process), `sample` (directly predicting the noisy sample`) or `v_prediction` (see section 2.4
-            https://imagen.research.google/video/paper.pdf)
-        thresholding (`bool`, default `False`):
-            whether to use the "dynamic thresholding" method (introduced by Imagen, https://arxiv.org/abs/2205.11487).
-            Note that the thresholding method is unsuitable for latent-space diffusion models (such as
-            stable-diffusion).
-        dynamic_thresholding_ratio (`float`, default `0.995`):
-            the ratio for the dynamic thresholding method. Default is `0.995`, the same as Imagen
-            (https://arxiv.org/abs/2205.11487). Valid only when `thresholding=True`.
-        sample_max_value (`float`, default `1.0`):
-            the threshold value for dynamic thresholding. Valid only when `thresholding=True`.
-        timestep_spacing (`str`, default `"leading"`):
-            The way the timesteps should be scaled. Refer to Table 2. of [Common Diffusion Noise Schedules and Sample
-            Steps are Flawed](https://arxiv.org/abs/2305.08891) for more information.
-        steps_offset (`int`, default `0`):
-            an offset added to the inference steps. You can use a combination of `offset=1` and
-            `set_alpha_to_one=False`, to make the last step use step 0 for the previous alpha product, as done in
-            stable diffusion.
+        num_train_timesteps (`int`, defaults to 1000):
+            The number of diffusion steps to train the model.
+        beta_start (`float`, defaults to 0.0001):
+            The starting `beta` value of inference.
+        beta_end (`float`, defaults to 0.02):
+            The final `beta` value.
+        beta_schedule (`str`, defaults to `"linear"`):
+            The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
+            `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
+        variance_type (`str`, defaults to `"fixed_small"`):
+            Clip the variance when adding noise to the denoised sample. Choose from `fixed_small`, `fixed_small_log`,
+            `fixed_large`, `fixed_large_log`, `learned` or `learned_range`.
+        clip_sample (`bool`, defaults to `True`):
+            Clip the predicted sample for numerical stability.
+        clip_sample_range (`float`, defaults to 1.0):
+            The maximum magnitude for sample clipping. Valid only when `clip_sample=True`.
+        prediction_type (`str`, defaults to `epsilon`, *optional*):
+            Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
+            `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen
+            Video](https://imagen.research.google/video/paper.pdf) paper).
+        thresholding (`bool`, defaults to `False`):
+            Whether to use the "dynamic thresholding" method. This is unsuitable for latent-space diffusion models such
+            as Stable Diffusion.
+        dynamic_thresholding_ratio (`float`, defaults to 0.995):
+            The ratio for the dynamic thresholding method. Valid only when `thresholding=True`.
+        sample_max_value (`float`, defaults to 1.0):
+            The threshold value for dynamic thresholding. Valid only when `thresholding=True`.
+        timestep_spacing (`str`, defaults to `"leading"`):
+            The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
+            Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
+        steps_offset (`int`, defaults to 0):
+            An offset added to the inference steps. You can use a combination of `offset=1` and
+            `set_alpha_to_one=False` to make the last step use step 0 for the previous alpha product like in Stable
+            Diffusion.
     """
 
     _compatibles = [e.name for e in KarrasDiffusionSchedulers]
@@ -198,11 +192,14 @@ class DDPMScheduler(SchedulerMixin, ConfigMixin):
         current timestep.
 
         Args:
-            sample (`torch.FloatTensor`): input sample
-            timestep (`int`, optional): current timestep
+            sample (`torch.FloatTensor`):
+                The input sample.
+            timestep (`int`, *optional*):
+                The current timestep in the diffusion chain.
 
         Returns:
-            `torch.FloatTensor`: scaled input sample
+            `torch.FloatTensor`:
+                A scaled input sample.
         """
         return sample
 
@@ -213,18 +210,18 @@ class DDPMScheduler(SchedulerMixin, ConfigMixin):
         timesteps: Optional[List[int]] = None,
     ):
         """
-        Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.
+        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
 
         Args:
-            num_inference_steps (`Optional[int]`):
-                the number of diffusion steps used when generating samples with a pre-trained model. If passed, then
+            num_inference_steps (`int`):
+                The number of diffusion steps used when generating samples with a pre-trained model. If used,
                 `timesteps` must be `None`.
-            device (`str` or `torch.device`, optional):
-                the device to which the timesteps are moved to.
-            custom_timesteps (`List[int]`, optional):
-                custom timesteps used to support arbitrary spacing between timesteps. If `None`, then the default
-                timestep spacing strategy of equal spacing between timesteps is used. If passed, `num_inference_steps`
-                must be `None`.
+            device (`str` or `torch.device`, *optional*):
+                The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
+            timesteps (`List[int]`, *optional*):
+                Custom timesteps used to support arbitrary spacing between timesteps. If `None`, then the default
+                timestep spacing strategy of equal spacing between timesteps is used. If `timesteps` is passed,
+                `num_inference_steps` must be `None`.
 
         """
         if num_inference_steps is not None and timesteps is not None:
@@ -364,21 +361,25 @@ class DDPMScheduler(SchedulerMixin, ConfigMixin):
         return_dict: bool = True,
     ) -> Union[DDPMSchedulerOutput, Tuple]:
         """
-        Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
+        Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
         process from the learned model outputs (most often the predicted noise).
 
         Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`int`): current discrete timestep in the diffusion chain.
+            model_output (`torch.FloatTensor`):
+                The direct output from learned diffusion model.
+            timestep (`float`):
+                The current discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
-            generator: random number generator.
-            return_dict (`bool`): option for returning tuple rather than DDPMSchedulerOutput class
+                A current instance of a sample created by the diffusion process.
+            generator (`torch.Generator`, *optional*):
+                A random number generator.
+            return_dict (`bool`, *optional*, defaults to `True`):
+                Whether or not to return a [`~schedulers.scheduling_ddpm.DDPMSchedulerOutput`] or `tuple`.
 
         Returns:
-            [`~schedulers.scheduling_utils.DDPMSchedulerOutput`] or `tuple`:
-            [`~schedulers.scheduling_utils.DDPMSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When
-            returning a tuple, the first element is the sample tensor.
+            [`~schedulers.scheduling_ddpm.DDPMSchedulerOutput`] or `tuple`:
+                If return_dict is `True`, [`~schedulers.scheduling_ddpm.DDPMSchedulerOutput`] is returned, otherwise a
+                tuple is returned where the first element is the sample tensor.
 
         """
         t = timestep

src/diffusers/schedulers/scheduling_ddpm_parallel.py

@@ -30,14 +30,14 @@ from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin
 # Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput
 class DDPMParallelSchedulerOutput(BaseOutput):
     """
-    Output class for the scheduler's step function output.
+    Output class for the scheduler's `step` function output.
 
     Args:
         prev_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
-            Computed sample (x_{t-1}) of previous timestep. `prev_sample` should be used as next model input in the
+            Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the
             denoising loop.
         pred_original_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
-            The predicted denoised sample (x_{0}) based on the model output from the current timestep.
+            The predicted denoised sample `(x_{0})` based on the model output from the current timestep.
             `pred_original_sample` can be used to preview progress or for guidance.
     """
 
@@ -203,11 +203,14 @@ class DDPMParallelScheduler(SchedulerMixin, ConfigMixin):
         current timestep.
 
         Args:
-            sample (`torch.FloatTensor`): input sample
-            timestep (`int`, optional): current timestep
+            sample (`torch.FloatTensor`):
+                The input sample.
+            timestep (`int`, *optional*):
+                The current timestep in the diffusion chain.
 
         Returns:
-            `torch.FloatTensor`: scaled input sample
+            `torch.FloatTensor`:
+                A scaled input sample.
         """
         return sample
 
@@ -219,18 +222,18 @@ class DDPMParallelScheduler(SchedulerMixin, ConfigMixin):
         timesteps: Optional[List[int]] = None,
     ):
         """
-        Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.
+        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
 
         Args:
-            num_inference_steps (`Optional[int]`):
-                the number of diffusion steps used when generating samples with a pre-trained model. If passed, then
+            num_inference_steps (`int`):
+                The number of diffusion steps used when generating samples with a pre-trained model. If used,
                 `timesteps` must be `None`.
-            device (`str` or `torch.device`, optional):
-                the device to which the timesteps are moved to.
-            custom_timesteps (`List[int]`, optional):
-                custom timesteps used to support arbitrary spacing between timesteps. If `None`, then the default
-                timestep spacing strategy of equal spacing between timesteps is used. If passed, `num_inference_steps`
-                must be `None`.
+            device (`str` or `torch.device`, *optional*):
+                The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
+            timesteps (`List[int]`, *optional*):
+                Custom timesteps used to support arbitrary spacing between timesteps. If `None`, then the default
+                timestep spacing strategy of equal spacing between timesteps is used. If `timesteps` is passed,
+                `num_inference_steps` must be `None`.
 
         """
         if num_inference_steps is not None and timesteps is not None:

src/diffusers/schedulers/scheduling_deis_multistep.py

@@ -72,63 +72,51 @@ def betas_for_alpha_bar(
 
 class DEISMultistepScheduler(SchedulerMixin, ConfigMixin):
     """
-    DEIS (https://arxiv.org/abs/2204.13902) is a fast high order solver for diffusion ODEs. We slightly modify the
-    polynomial fitting formula in log-rho space instead of the original linear t space in DEIS paper. The modification
-    enjoys closed-form coefficients for exponential multistep update instead of replying on the numerical solver. More
-    variants of DEIS can be found in https://github.com/qsh-zh/deis.
+    `DEISMultistepScheduler` is a fast high order solver for diffusion ordinary differential equations (ODEs).
 
-    Currently, we support the log-rho multistep DEIS. We recommend to use `solver_order=2 / 3` while `solver_order=1`
-    reduces to DDIM.
-
-    We also support the "dynamic thresholding" method in Imagen (https://arxiv.org/abs/2205.11487). For pixel-space
-    diffusion models, you can set `thresholding=True` to use the dynamic thresholding.
-
-    [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
-    function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`.
-    [`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and
-    [`~SchedulerMixin.from_pretrained`] functions.
+    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
+    methods the library implements for all schedulers such as loading and saving.
 
     Args:
-        num_train_timesteps (`int`): number of diffusion steps used to train the model.
-        beta_start (`float`): the starting `beta` value of inference.
-        beta_end (`float`): the final `beta` value.
-        beta_schedule (`str`):
-            the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
+        num_train_timesteps (`int`, defaults to 1000):
+            The number of diffusion steps to train the model.
+        beta_start (`float`, defaults to 0.0001):
+            The starting `beta` value of inference.
+        beta_end (`float`, defaults to 0.02):
+            The final `beta` value.
+        beta_schedule (`str`, defaults to `"linear"`):
+            The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
             `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
-        trained_betas (`np.ndarray`, optional):
-            option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
-        solver_order (`int`, default `2`):
-            the order of DEIS; can be `1` or `2` or `3`. We recommend to use `solver_order=2` for guided sampling, and
-            `solver_order=3` for unconditional sampling.
-        prediction_type (`str`, default `epsilon`):
-            indicates whether the model predicts the noise (epsilon), or the data / `x0`. One of `epsilon`, `sample`,
-            or `v-prediction`.
-        thresholding (`bool`, default `False`):
-            whether to use the "dynamic thresholding" method (introduced by Imagen, https://arxiv.org/abs/2205.11487).
-            Note that the thresholding method is unsuitable for latent-space diffusion models (such as
-            stable-diffusion).
-        dynamic_thresholding_ratio (`float`, default `0.995`):
-            the ratio for the dynamic thresholding method. Default is `0.995`, the same as Imagen
-            (https://arxiv.org/abs/2205.11487).
-        sample_max_value (`float`, default `1.0`):
-            the threshold value for dynamic thresholding. Valid only when `thresholding=True`
-        algorithm_type (`str`, default `deis`):
-            the algorithm type for the solver. current we support multistep deis, we will add other variants of DEIS in
-            the future
-        lower_order_final (`bool`, default `True`):
-            whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. We empirically
-            find this trick can stabilize the sampling of DEIS for steps < 15, especially for steps <= 10.
+        trained_betas (`np.ndarray`, *optional*):
+            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
+        solver_order (`int`, defaults to 2):
+            The DEIS order which can be `1` or `2` or `3`. It is recommended to use `solver_order=2` for guided
+            sampling, and `solver_order=3` for unconditional sampling.
+        prediction_type (`str`, defaults to `epsilon`):
+            Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
+            `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen
+            Video](https://imagen.research.google/video/paper.pdf) paper).
+        thresholding (`bool`, defaults to `False`):
+            Whether to use the "dynamic thresholding" method. This is unsuitable for latent-space diffusion models such
+            as Stable Diffusion.
+        dynamic_thresholding_ratio (`float`, defaults to 0.995):
+            The ratio for the dynamic thresholding method. Valid only when `thresholding=True`.
+        sample_max_value (`float`, defaults to 1.0):
+            The threshold value for dynamic thresholding. Valid only when `thresholding=True`.
+        algorithm_type (`str`, defaults to `deis`):
+            The algorithm type for the solver.
+        lower_order_final (`bool`, defaults to `True`):
+            Whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps.
         use_karras_sigmas (`bool`, *optional*, defaults to `False`):
-             This parameter controls whether to use Karras sigmas (Karras et al. (2022) scheme) for step sizes in the
-             noise schedule during the sampling process. If True, the sigmas will be determined according to a sequence
-             of noise levels {σi} as defined in Equation (5) of the paper https://arxiv.org/pdf/2206.00364.pdf.
-        timestep_spacing (`str`, default `"linspace"`):
-            The way the timesteps should be scaled. Refer to Table 2. of [Common Diffusion Noise Schedules and Sample
-            Steps are Flawed](https://arxiv.org/abs/2305.08891) for more information.
-        steps_offset (`int`, default `0`):
-            an offset added to the inference steps. You can use a combination of `offset=1` and
-            `set_alpha_to_one=False`, to make the last step use step 0 for the previous alpha product, as done in
-            stable diffusion.
+             Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. If `True`,
+             the sigmas are determined according to a sequence of noise levels {σi}.
+        timestep_spacing (`str`, defaults to `"linspace"`):
+            The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
+            Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
+        steps_offset (`int`, defaults to 0):
+            An offset added to the inference steps. You can use a combination of `offset=1` and
+            `set_alpha_to_one=False` to make the last step use step 0 for the previous alpha product like in Stable
+            Diffusion.
     """
 
     _compatibles = [e.name for e in KarrasDiffusionSchedulers]
@@ -201,13 +189,13 @@ class DEISMultistepScheduler(SchedulerMixin, ConfigMixin):
 
     def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
         """
-        Sets the timesteps used for the diffusion chain. Supporting function to be run before inference.
+        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
 
         Args:
             num_inference_steps (`int`):
-                the number of diffusion steps used when generating samples with a pre-trained model.
-            device (`str` or `torch.device`, optional):
-                the device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
+                The number of diffusion steps used when generating samples with a pre-trained model.
+            device (`str` or `torch.device`, *optional*):
+                The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
         """
         # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
         if self.config.timestep_spacing == "linspace":
@@ -296,16 +284,19 @@ class DEISMultistepScheduler(SchedulerMixin, ConfigMixin):
         self, model_output: torch.FloatTensor, timestep: int, sample: torch.FloatTensor
     ) -> torch.FloatTensor:
         """
-        Convert the model output to the corresponding type that the algorithm DEIS needs.
+        Convert the model output to the corresponding type the DEIS algorithm needs.
 
         Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`int`): current discrete timestep in the diffusion chain.
+            model_output (`torch.FloatTensor`):
+                The direct output from the learned diffusion model.
+            timestep (`int`):
+                The current discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
+                A current instance of a sample created by the diffusion process.
 
         Returns:
-            `torch.FloatTensor`: the converted model output.
+            `torch.FloatTensor`:
+                The converted model output.
         """
         if self.config.prediction_type == "epsilon":
             alpha_t, sigma_t = self.alpha_t[timestep], self.sigma_t[timestep]
@@ -341,14 +332,18 @@ class DEISMultistepScheduler(SchedulerMixin, ConfigMixin):
         One step for the first-order DEIS (equivalent to DDIM).
 
         Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`int`): current discrete timestep in the diffusion chain.
-            prev_timestep (`int`): previous discrete timestep in the diffusion chain.
+            model_output (`torch.FloatTensor`):
+                The direct output from the learned diffusion model.
+            timestep (`int`):
+                The current discrete timestep in the diffusion chain.
+            prev_timestep (`int`):
+                The previous discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
+                A current instance of a sample created by the diffusion process.
 
         Returns:
-            `torch.FloatTensor`: the sample tensor at the previous timestep.
+            `torch.FloatTensor`:
+                The sample tensor at the previous timestep.
         """
         lambda_t, lambda_s = self.lambda_t[prev_timestep], self.lambda_t[timestep]
         alpha_t, alpha_s = self.alpha_t[prev_timestep], self.alpha_t[timestep]
@@ -372,14 +367,17 @@ class DEISMultistepScheduler(SchedulerMixin, ConfigMixin):
 
         Args:
             model_output_list (`List[torch.FloatTensor]`):
-                direct outputs from learned diffusion model at current and latter timesteps.
-            timestep (`int`): current and latter discrete timestep in the diffusion chain.
-            prev_timestep (`int`): previous discrete timestep in the diffusion chain.
+                The direct outputs from learned diffusion model at current and latter timesteps.
+            timestep (`int`):
+                The current and latter discrete timestep in the diffusion chain.
+            prev_timestep (`int`):
+                The previous discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
+                A current instance of a sample created by the diffusion process.
 
         Returns:
-            `torch.FloatTensor`: the sample tensor at the previous timestep.
+            `torch.FloatTensor`:
+                The sample tensor at the previous timestep.
         """
         t, s0, s1 = prev_timestep, timestep_list[-1], timestep_list[-2]
         m0, m1 = model_output_list[-1], model_output_list[-2]
@@ -414,14 +412,17 @@ class DEISMultistepScheduler(SchedulerMixin, ConfigMixin):
 
         Args:
             model_output_list (`List[torch.FloatTensor]`):
-                direct outputs from learned diffusion model at current and latter timesteps.
-            timestep (`int`): current and latter discrete timestep in the diffusion chain.
-            prev_timestep (`int`): previous discrete timestep in the diffusion chain.
+                The direct outputs from learned diffusion model at current and latter timesteps.
+            timestep (`int`):
+                The current and latter discrete timestep in the diffusion chain.
+            prev_timestep (`int`):
+                The previous discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
+                A current instance of a sample created by diffusion process.
 
         Returns:
-            `torch.FloatTensor`: the sample tensor at the previous timestep.
+            `torch.FloatTensor`:
+                The sample tensor at the previous timestep.
         """
         t, s0, s1, s2 = prev_timestep, timestep_list[-1], timestep_list[-2], timestep_list[-3]
         m0, m1, m2 = model_output_list[-1], model_output_list[-2], model_output_list[-3]
@@ -467,18 +468,23 @@ class DEISMultistepScheduler(SchedulerMixin, ConfigMixin):
         return_dict: bool = True,
     ) -> Union[SchedulerOutput, Tuple]:
         """
-        Step function propagating the sample with the multistep DEIS.
+        Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
+        the multistep DEIS.
 
         Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`int`): current discrete timestep in the diffusion chain.
+            model_output (`torch.FloatTensor`):
+                The direct output from learned diffusion model.
+            timestep (`float`):
+                The current discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
-            return_dict (`bool`): option for returning tuple rather than SchedulerOutput class
+                A current instance of a sample created by the diffusion process.
+            return_dict (`bool`):
+                Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`.
 
         Returns:
-            [`~scheduling_utils.SchedulerOutput`] or `tuple`: [`~scheduling_utils.SchedulerOutput`] if `return_dict` is
-            True, otherwise a `tuple`. When returning a tuple, the first element is the sample tensor.
+            [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
+                If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a
+                tuple is returned where the first element is the sample tensor.
 
         """
         if self.num_inference_steps is None:
@@ -533,10 +539,12 @@ class DEISMultistepScheduler(SchedulerMixin, ConfigMixin):
         current timestep.
 
         Args:
-            sample (`torch.FloatTensor`): input sample
+            sample (`torch.FloatTensor`):
+                The input sample.
 
         Returns:
-            `torch.FloatTensor`: scaled input sample
+            `torch.FloatTensor`:
+                A scaled input sample.
         """
         return sample
 

src/diffusers/schedulers/scheduling_dpmsolver_multistep.py

@@ -72,90 +72,66 @@ def betas_for_alpha_bar(
 
 class DPMSolverMultistepScheduler(SchedulerMixin, ConfigMixin):
     """
-    DPM-Solver (and the improved version DPM-Solver++) is a fast dedicated high-order solver for diffusion ODEs with
-    the convergence order guarantee. Empirically, sampling by DPM-Solver with only 20 steps can generate high-quality
-    samples, and it can generate quite good samples even in only 10 steps.
+    `DPMSolverMultistepScheduler` is a fast dedicated high-order solver for diffusion ODEs.
 
-    For more details, see the original paper: https://arxiv.org/abs/2206.00927 and https://arxiv.org/abs/2211.01095
-
-    Currently, we support the multistep DPM-Solver for both noise prediction models and data prediction models. We
-    recommend to use `solver_order=2` for guided sampling, and `solver_order=3` for unconditional sampling.
-
-    We also support the "dynamic thresholding" method in Imagen (https://arxiv.org/abs/2205.11487). For pixel-space
-    diffusion models, you can set both `algorithm_type="dpmsolver++"` and `thresholding=True` to use the dynamic
-    thresholding. Note that the thresholding method is unsuitable for latent-space diffusion models (such as
-    stable-diffusion).
-
-    We also support the SDE variant of DPM-Solver and DPM-Solver++, which is a fast SDE solver for the reverse
-    diffusion SDE. Currently we only support the first-order and second-order solvers. We recommend using the
-    second-order `sde-dpmsolver++`.
-
-    [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
-    function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`.
-    [`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and
-    [`~SchedulerMixin.from_pretrained`] functions.
+    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
+    methods the library implements for all schedulers such as loading and saving.
 
     Args:
-        num_train_timesteps (`int`): number of diffusion steps used to train the model.
-        beta_start (`float`): the starting `beta` value of inference.
-        beta_end (`float`): the final `beta` value.
-        beta_schedule (`str`):
-            the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
+        num_train_timesteps (`int`, defaults to 1000):
+            The number of diffusion steps to train the model.
+        beta_start (`float`, defaults to 0.0001):
+            The starting `beta` value of inference.
+        beta_end (`float`, defaults to 0.02):
+            The final `beta` value.
+        beta_schedule (`str`, defaults to `"linear"`):
+            The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
             `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
-        trained_betas (`np.ndarray`, optional):
-            option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
-        solver_order (`int`, default `2`):
-            the order of DPM-Solver; can be `1` or `2` or `3`. We recommend to use `solver_order=2` for guided
+        trained_betas (`np.ndarray`, *optional*):
+            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
+        solver_order (`int`, defaults to 2):
+            The DPMSolver order which can be `1` or `2` or `3`. It is recommended to use `solver_order=2` for guided
             sampling, and `solver_order=3` for unconditional sampling.
-        prediction_type (`str`, default `epsilon`, optional):
-            prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion
-            process), `sample` (directly predicting the noisy sample`) or `v_prediction` (see section 2.4
-            https://imagen.research.google/video/paper.pdf)
-        thresholding (`bool`, default `False`):
-            whether to use the "dynamic thresholding" method (introduced by Imagen, https://arxiv.org/abs/2205.11487).
-            For pixel-space diffusion models, you can set both `algorithm_type=dpmsolver++` and `thresholding=True` to
-            use the dynamic thresholding. Note that the thresholding method is unsuitable for latent-space diffusion
-            models (such as stable-diffusion).
-        dynamic_thresholding_ratio (`float`, default `0.995`):
-            the ratio for the dynamic thresholding method. Default is `0.995`, the same as Imagen
-            (https://arxiv.org/abs/2205.11487).
-        sample_max_value (`float`, default `1.0`):
-            the threshold value for dynamic thresholding. Valid only when `thresholding=True` and
-            `algorithm_type="dpmsolver++`.
-        algorithm_type (`str`, default `dpmsolver++`):
-            the algorithm type for the solver. Either `dpmsolver` or `dpmsolver++` or `sde-dpmsolver` or
-            `sde-dpmsolver++`. The `dpmsolver` type implements the algorithms in https://arxiv.org/abs/2206.00927, and
-            the `dpmsolver++` type implements the algorithms in https://arxiv.org/abs/2211.01095. We recommend to use
-            `dpmsolver++` or `sde-dpmsolver++` with `solver_order=2` for guided sampling (e.g. stable-diffusion).
-        solver_type (`str`, default `midpoint`):
-            the solver type for the second-order solver. Either `midpoint` or `heun`. The solver type slightly affects
-            the sample quality, especially for small number of steps. We empirically find that `midpoint` solvers are
-            slightly better, so we recommend to use the `midpoint` type.
-        lower_order_final (`bool`, default `True`):
-            whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. We empirically
-            find this trick can stabilize the sampling of DPM-Solver for steps < 15, especially for steps <= 10.
+        prediction_type (`str`, defaults to `epsilon`, *optional*):
+            Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
+            `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen
+            Video](https://imagen.research.google/video/paper.pdf) paper).
+        thresholding (`bool`, defaults to `False`):
+            Whether to use the "dynamic thresholding" method. This is unsuitable for latent-space diffusion models such
+            as Stable Diffusion.
+        dynamic_thresholding_ratio (`float`, defaults to 0.995):
+            The ratio for the dynamic thresholding method. Valid only when `thresholding=True`.
+        sample_max_value (`float`, defaults to 1.0):
+            The threshold value for dynamic thresholding. Valid only when `thresholding=True` and
+            `algorithm_type="dpmsolver++"`.
+        algorithm_type (`str`, defaults to `dpmsolver++`):
+            Algorithm type for the solver; can be `dpmsolver`, `dpmsolver++`, `sde-dpmsolver` or `sde-dpmsolver++`. The
+            `dpmsolver` type implements the algorithms in the [DPMSolver](https://huggingface.co/papers/2206.00927)
+            paper, and the `dpmsolver++` type implements the algorithms in the
+            [DPMSolver++](https://huggingface.co/papers/2211.01095) paper. It is recommended to use `dpmsolver++` or
+            `sde-dpmsolver++` with `solver_order=2` for guided sampling like in Stable Diffusion.
+        solver_type (`str`, defaults to `midpoint`):
+            Solver type for the second-order solver; can be `midpoint` or `heun`. The solver type slightly affects the
+            sample quality, especially for a small number of steps. It is recommended to use `midpoint` solvers.
+        lower_order_final (`bool`, defaults to `True`):
+            Whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. This can
+            stabilize the sampling of DPMSolver for steps < 15, especially for steps <= 10.
         use_karras_sigmas (`bool`, *optional*, defaults to `False`):
-             This parameter controls whether to use Karras sigmas (Karras et al. (2022) scheme) for step sizes in the
-             noise schedule during the sampling process. If True, the sigmas will be determined according to a sequence
-             of noise levels {σi} as defined in Equation (5) of the paper https://arxiv.org/pdf/2206.00364.pdf.
-        lambda_min_clipped (`float`, default `-inf`):
-            the clipping threshold for the minimum value of lambda(t) for numerical stability. This is critical for
-            cosine (squaredcos_cap_v2) noise schedule.
+            Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. If `True`,
+            the sigmas are determined according to a sequence of noise levels {σi}.
+        lambda_min_clipped (`float`, defaults to `-inf`):
+            Clipping threshold for the minimum value of `lambda(t)` for numerical stability. This is critical for the
+            cosine (`squaredcos_cap_v2`) noise schedule.
         variance_type (`str`, *optional*):
-            Set to "learned" or "learned_range" for diffusion models that predict variance. For example, OpenAI's
-            guided-diffusion (https://github.com/openai/guided-diffusion) predicts both mean and variance of the
-            Gaussian distribution in the model's output. DPM-Solver only needs the "mean" output because it is based on
-            diffusion ODEs. whether the model's output contains the predicted Gaussian variance. For example, OpenAI's
-            guided-diffusion (https://github.com/openai/guided-diffusion) predicts both mean and variance of the
-            Gaussian distribution in the model's output. DPM-Solver only needs the "mean" output because it is based on
-            diffusion ODEs.
-        timestep_spacing (`str`, default `"linspace"`):
-            The way the timesteps should be scaled. Refer to Table 2. of [Common Diffusion Noise Schedules and Sample
-            Steps are Flawed](https://arxiv.org/abs/2305.08891) for more information.
-        steps_offset (`int`, default `0`):
-            an offset added to the inference steps. You can use a combination of `offset=1` and
-            `set_alpha_to_one=False`, to make the last step use step 0 for the previous alpha product, as done in
-            stable diffusion.
+            Set to "learned" or "learned_range" for diffusion models that predict variance. If set, the model's output
+            contains the predicted Gaussian variance.
+        timestep_spacing (`str`, defaults to `"linspace"`):
+            The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
+            Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
+        steps_offset (`int`, defaults to 0):
+            An offset added to the inference steps. You can use a combination of `offset=1` and
+            `set_alpha_to_one=False` to make the last step use step 0 for the previous alpha product like in Stable
+            Diffusion.
     """
 
     _compatibles = [e.name for e in KarrasDiffusionSchedulers]
@@ -230,13 +206,13 @@ class DPMSolverMultistepScheduler(SchedulerMixin, ConfigMixin):
 
     def set_timesteps(self, num_inference_steps: int = None, device: Union[str, torch.device] = None):
         """
-        Sets the timesteps used for the diffusion chain. Supporting function to be run before inference.
+        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
 
         Args:
             num_inference_steps (`int`):
-                the number of diffusion steps used when generating samples with a pre-trained model.
-            device (`str` or `torch.device`, optional):
-                the device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
+                The number of diffusion steps used when generating samples with a pre-trained model.
+            device (`str` or `torch.device`, *optional*):
+                The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
         """
         # Clipping the minimum of all lambda(t) for numerical stability.
         # This is critical for cosine (squaredcos_cap_v2) noise schedule.
@@ -365,23 +341,28 @@ class DPMSolverMultistepScheduler(SchedulerMixin, ConfigMixin):
         self, model_output: torch.FloatTensor, timestep: int, sample: torch.FloatTensor
     ) -> torch.FloatTensor:
         """
-        Convert the model output to the corresponding type that the algorithm (DPM-Solver / DPM-Solver++) needs.
+        Convert the model output to the corresponding type the DPMSolver/DPMSolver++ algorithm needs. DPM-Solver is
+        designed to discretize an integral of the noise prediction model, and DPM-Solver++ is designed to discretize an
+        integral of the data prediction model.
 
-        DPM-Solver is designed to discretize an integral of the noise prediction model, and DPM-Solver++ is designed to
-        discretize an integral of the data prediction model. So we need to first convert the model output to the
-        corresponding type to match the algorithm.
+        <Tip>
 
-        Note that the algorithm type and the model type is decoupled. That is to say, we can use either DPM-Solver or
-        DPM-Solver++ for both noise prediction model and data prediction model.
+        The algorithm and model type are decoupled. You can use either DPMSolver or DPMSolver++ for both noise
+        prediction and data prediction models.
+
+        </Tip>
 
         Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`int`): current discrete timestep in the diffusion chain.
+            model_output (`torch.FloatTensor`):
+                The direct output from the learned diffusion model.
+            timestep (`int`):
+                The current discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
+                A current instance of a sample created by the diffusion process.
 
         Returns:
-            `torch.FloatTensor`: the converted model output.
+            `torch.FloatTensor`:
+                The converted model output.
         """
 
         # DPM-Solver++ needs to solve an integral of the data prediction model.
@@ -445,19 +426,21 @@ class DPMSolverMultistepScheduler(SchedulerMixin, ConfigMixin):
         noise: Optional[torch.FloatTensor] = None,
     ) -> torch.FloatTensor:
         """
-        One step for the first-order DPM-Solver (equivalent to DDIM).
-
-        See https://arxiv.org/abs/2206.00927 for the detailed derivation.
+        One step for the first-order DPMSolver (equivalent to DDIM).
 
         Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`int`): current discrete timestep in the diffusion chain.
-            prev_timestep (`int`): previous discrete timestep in the diffusion chain.
+            model_output (`torch.FloatTensor`):
+                The direct output from the learned diffusion model.
+            timestep (`int`):
+                The current discrete timestep in the diffusion chain.
+            prev_timestep (`int`):
+                The previous discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
+                A current instance of a sample created by the diffusion process.
 
         Returns:
-            `torch.FloatTensor`: the sample tensor at the previous timestep.
+            `torch.FloatTensor`:
+                The sample tensor at the previous timestep.
         """
         lambda_t, lambda_s = self.lambda_t[prev_timestep], self.lambda_t[timestep]
         alpha_t, alpha_s = self.alpha_t[prev_timestep], self.alpha_t[timestep]
@@ -492,18 +475,21 @@ class DPMSolverMultistepScheduler(SchedulerMixin, ConfigMixin):
         noise: Optional[torch.FloatTensor] = None,
     ) -> torch.FloatTensor:
         """
-        One step for the second-order multistep DPM-Solver.
+        One step for the second-order multistep DPMSolver.
 
         Args:
             model_output_list (`List[torch.FloatTensor]`):
-                direct outputs from learned diffusion model at current and latter timesteps.
-            timestep (`int`): current and latter discrete timestep in the diffusion chain.
-            prev_timestep (`int`): previous discrete timestep in the diffusion chain.
+                The direct outputs from learned diffusion model at current and latter timesteps.
+            timestep (`int`):
+                The current and latter discrete timestep in the diffusion chain.
+            prev_timestep (`int`):
+                The previous discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
+                A current instance of a sample created by the diffusion process.
 
         Returns:
-            `torch.FloatTensor`: the sample tensor at the previous timestep.
+            `torch.FloatTensor`:
+                The sample tensor at the previous timestep.
         """
         t, s0, s1 = prev_timestep, timestep_list[-1], timestep_list[-2]
         m0, m1 = model_output_list[-1], model_output_list[-2]
@@ -583,18 +569,21 @@ class DPMSolverMultistepScheduler(SchedulerMixin, ConfigMixin):
         sample: torch.FloatTensor,
     ) -> torch.FloatTensor:
         """
-        One step for the third-order multistep DPM-Solver.
+        One step for the third-order multistep DPMSolver.
 
         Args:
             model_output_list (`List[torch.FloatTensor]`):
-                direct outputs from learned diffusion model at current and latter timesteps.
-            timestep (`int`): current and latter discrete timestep in the diffusion chain.
-            prev_timestep (`int`): previous discrete timestep in the diffusion chain.
+                The direct outputs from learned diffusion model at current and latter timesteps.
+            timestep (`int`):
+                The current and latter discrete timestep in the diffusion chain.
+            prev_timestep (`int`):
+                The previous discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
+                A current instance of a sample created by diffusion process.
 
         Returns:
-            `torch.FloatTensor`: the sample tensor at the previous timestep.
+            `torch.FloatTensor`:
+                The sample tensor at the previous timestep.
         """
         t, s0, s1, s2 = prev_timestep, timestep_list[-1], timestep_list[-2], timestep_list[-3]
         m0, m1, m2 = model_output_list[-1], model_output_list[-2], model_output_list[-3]
@@ -639,18 +628,25 @@ class DPMSolverMultistepScheduler(SchedulerMixin, ConfigMixin):
         return_dict: bool = True,
     ) -> Union[SchedulerOutput, Tuple]:
         """
-        Step function propagating the sample with the multistep DPM-Solver.
+        Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
+        the multistep DPMSolver.
 
         Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`int`): current discrete timestep in the diffusion chain.
+            model_output (`torch.FloatTensor`):
+                The direct output from learned diffusion model.
+            timestep (`int`):
+                The current discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
-            return_dict (`bool`): option for returning tuple rather than SchedulerOutput class
+                A current instance of a sample created by the diffusion process.
+            generator (`torch.Generator`, *optional*):
+                A random number generator.
+            return_dict (`bool`):
+                Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`.
 
         Returns:
-            [`~scheduling_utils.SchedulerOutput`] or `tuple`: [`~scheduling_utils.SchedulerOutput`] if `return_dict` is
-            True, otherwise a `tuple`. When returning a tuple, the first element is the sample tensor.
+            [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
+                If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a
+                tuple is returned where the first element is the sample tensor.
 
         """
         if self.num_inference_steps is None:
@@ -714,10 +710,12 @@ class DPMSolverMultistepScheduler(SchedulerMixin, ConfigMixin):
         current timestep.
 
         Args:
-            sample (`torch.FloatTensor`): input sample
+            sample (`torch.FloatTensor`):
+                The input sample.
 
         Returns:
-            `torch.FloatTensor`: scaled input sample
+            `torch.FloatTensor`:
+                A scaled input sample.
         """
         return sample
 

src/diffusers/schedulers/scheduling_dpmsolver_multistep_inverse.py

@@ -72,79 +72,66 @@ def betas_for_alpha_bar(
 
 class DPMSolverMultistepInverseScheduler(SchedulerMixin, ConfigMixin):
     """
-    DPMSolverMultistepInverseScheduler is the reverse scheduler of [`DPMSolverMultistepScheduler`].
+    `DPMSolverMultistepInverseScheduler` is the reverse scheduler of [`DPMSolverMultistepScheduler`].
 
-    We also support the "dynamic thresholding" method in Imagen (https://arxiv.org/abs/2205.11487). For pixel-space
-    diffusion models, you can set both `algorithm_type="dpmsolver++"` and `thresholding=True` to use the dynamic
-    thresholding. Note that the thresholding method is unsuitable for latent-space diffusion models (such as
-    stable-diffusion).
-
-    [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
-    function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`.
-    [`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and
-    [`~SchedulerMixin.from_pretrained`] functions.
+    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
+    methods the library implements for all schedulers such as loading and saving.
 
     Args:
-        num_train_timesteps (`int`): number of diffusion steps used to train the model.
-        beta_start (`float`): the starting `beta` value of inference.
-        beta_end (`float`): the final `beta` value.
-        beta_schedule (`str`):
-            the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
+        num_train_timesteps (`int`, defaults to 1000):
+            The number of diffusion steps to train the model.
+        beta_start (`float`, defaults to 0.0001):
+            The starting `beta` value of inference.
+        beta_end (`float`, defaults to 0.02):
+            The final `beta` value.
+        beta_schedule (`str`, defaults to `"linear"`):
+            The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
             `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
-        trained_betas (`np.ndarray`, optional):
-            option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
-        solver_order (`int`, default `2`):
-            the order of DPM-Solver; can be `1` or `2` or `3`. We recommend to use `solver_order=2` for guided
+        trained_betas (`np.ndarray`, *optional*):
+            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
+        solver_order (`int`, defaults to 2):
+            The DPMSolver order which can be `1` or `2` or `3`. It is recommended to use `solver_order=2` for guided
             sampling, and `solver_order=3` for unconditional sampling.
-        prediction_type (`str`, default `epsilon`, optional):
-            prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion
-            process), `sample` (directly predicting the noisy sample`) or `v_prediction` (see section 2.4
-            https://imagen.research.google/video/paper.pdf)
-        thresholding (`bool`, default `False`):
-            whether to use the "dynamic thresholding" method (introduced by Imagen, https://arxiv.org/abs/2205.11487).
-            For pixel-space diffusion models, you can set both `algorithm_type=dpmsolver++` and `thresholding=True` to
-            use the dynamic thresholding. Note that the thresholding method is unsuitable for latent-space diffusion
-            models (such as stable-diffusion).
-        dynamic_thresholding_ratio (`float`, default `0.995`):
-            the ratio for the dynamic thresholding method. Default is `0.995`, the same as Imagen
-            (https://arxiv.org/abs/2205.11487).
-        sample_max_value (`float`, default `1.0`):
-            the threshold value for dynamic thresholding. Valid only when `thresholding=True` and
-            `algorithm_type="dpmsolver++`.
-        algorithm_type (`str`, default `dpmsolver++`):
-            the algorithm type for the solver. Either `dpmsolver` or `dpmsolver++` or `sde-dpmsolver` or
-            `sde-dpmsolver++`. The `dpmsolver` type implements the algorithms in https://arxiv.org/abs/2206.00927, and
-            the `dpmsolver++` type implements the algorithms in https://arxiv.org/abs/2211.01095. We recommend to use
-            `dpmsolver++` or `sde-dpmsolver++` with `solver_order=2` for guided sampling (e.g. stable-diffusion).
-        solver_type (`str`, default `midpoint`):
-            the solver type for the second-order solver. Either `midpoint` or `heun`. The solver type slightly affects
-            the sample quality, especially for small number of steps. We empirically find that `midpoint` solvers are
-            slightly better, so we recommend to use the `midpoint` type.
-        lower_order_final (`bool`, default `True`):
-            whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. We empirically
-            find this trick can stabilize the sampling of DPM-Solver for steps < 15, especially for steps <= 10.
+        prediction_type (`str`, defaults to `epsilon`, *optional*):
+            Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
+            `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen
+            Video](https://imagen.research.google/video/paper.pdf) paper).
+        thresholding (`bool`, defaults to `False`):
+            Whether to use the "dynamic thresholding" method. This is unsuitable for latent-space diffusion models such
+            as Stable Diffusion.
+        dynamic_thresholding_ratio (`float`, defaults to 0.995):
+            The ratio for the dynamic thresholding method. Valid only when `thresholding=True`.
+        sample_max_value (`float`, defaults to 1.0):
+            The threshold value for dynamic thresholding. Valid only when `thresholding=True` and
+            `algorithm_type="dpmsolver++"`.
+        algorithm_type (`str`, defaults to `dpmsolver++`):
+            Algorithm type for the solver; can be `dpmsolver`, `dpmsolver++`, `sde-dpmsolver` or `sde-dpmsolver++`. The
+            `dpmsolver` type implements the algorithms in the [DPMSolver](https://huggingface.co/papers/2206.00927)
+            paper, and the `dpmsolver++` type implements the algorithms in the
+            [DPMSolver++](https://huggingface.co/papers/2211.01095) paper. It is recommended to use `dpmsolver++` or
+            `sde-dpmsolver++` with `solver_order=2` for guided sampling like in Stable Diffusion.
+        solver_type (`str`, defaults to `midpoint`):
+            Solver type for the second-order solver; can be `midpoint` or `heun`. The solver type slightly affects the
+            sample quality, especially for a small number of steps. It is recommended to use `midpoint` solvers.
+        lower_order_final (`bool`, defaults to `True`):
+            Whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. This can
+            stabilize the sampling of DPMSolver for steps < 15, especially for steps <= 10.
         use_karras_sigmas (`bool`, *optional*, defaults to `False`):
-             This parameter controls whether to use Karras sigmas (Karras et al. (2022) scheme) for step sizes in the
-             noise schedule during the sampling process. If True, the sigmas will be determined according to a sequence
-             of noise levels {σi} as defined in Equation (5) of the paper https://arxiv.org/pdf/2206.00364.pdf.
-        lambda_min_clipped (`float`, default `-inf`):
-            the clipping threshold for the minimum value of lambda(t) for numerical stability. This is critical for
-            cosine (squaredcos_cap_v2) noise schedule.
+            Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. If `True`,
+            the sigmas are determined according to a sequence of noise levels {σi}.
+        lambda_min_clipped (`float`, defaults to `-inf`):
+            Clipping threshold for the minimum value of `lambda(t)` for numerical stability. This is critical for the
+            cosine (`squaredcos_cap_v2`) noise schedule.
         variance_type (`str`, *optional*):
-            Set to "learned" or "learned_range" for diffusion models that predict variance. For example, OpenAI's
-            guided-diffusion (https://github.com/openai/guided-diffusion) predicts both mean and variance of the
-            Gaussian distribution in the model's output. DPM-Solver only needs the "mean" output because it is based on
-            diffusion ODEs. whether the model's output contains the predicted Gaussian variance. For example, OpenAI's
-            guided-diffusion (https://github.com/openai/guided-diffusion) predicts both mean and variance of the
-            Gaussian distribution in the model's output. DPM-Solver only needs the "mean" output because it is based on
-            diffusion ODEs.
-        timestep_spacing (`str`, default `"linspace"`):
-            The way the timesteps should be scaled. Refer to Table 2. of [Common Diffusion Noise Schedules and Sample
-            Steps are Flawed](https://arxiv.org/abs/2305.08891) for more information.
-        steps_offset (`int`, default `0`):
-            an offset added to the inference steps. You can use a combination of `offset=1` and
-            `set_alpha_to_one=False`, to make the last step use step 0 for the previous alpha product, as done in
-            stable diffusion.
+            Set to "learned" or "learned_range" for diffusion models that predict variance. If set, the model's output
+            contains the predicted Gaussian variance.
+        timestep_spacing (`str`, defaults to `"linspace"`):
+            The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
+            Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
+        steps_offset (`int`, defaults to 0):
+            An offset added to the inference steps. You can use a combination of `offset=1` and
+            `set_alpha_to_one=False` to make the last step use step 0 for the previous alpha product like in Stable
+            Diffusion.
     """
 
     _compatibles = [e.name for e in KarrasDiffusionSchedulers]
@@ -220,13 +207,13 @@ class DPMSolverMultistepInverseScheduler(SchedulerMixin, ConfigMixin):
 
     def set_timesteps(self, num_inference_steps: int = None, device: Union[str, torch.device] = None):
         """
-        Sets the timesteps used for the diffusion chain. Supporting function to be run before inference.
+        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
 
         Args:
             num_inference_steps (`int`):
-                the number of diffusion steps used when generating samples with a pre-trained model.
-            device (`str` or `torch.device`, optional):
-                the device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
+                The number of diffusion steps used when generating samples with a pre-trained model.
+            device (`str` or `torch.device`, *optional*):
+                The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
         """
         # Clipping the minimum of all lambda(t) for numerical stability.
         # This is critical for cosine (squaredcos_cap_v2) noise schedule.
@@ -357,23 +344,28 @@ class DPMSolverMultistepInverseScheduler(SchedulerMixin, ConfigMixin):
         self, model_output: torch.FloatTensor, timestep: int, sample: torch.FloatTensor
     ) -> torch.FloatTensor:
         """
-        Convert the model output to the corresponding type that the algorithm (DPM-Solver / DPM-Solver++) needs.
+        Convert the model output to the corresponding type the DPMSolver/DPMSolver++ algorithm needs. DPM-Solver is
+        designed to discretize an integral of the noise prediction model, and DPM-Solver++ is designed to discretize an
+        integral of the data prediction model.
+
+        <Tip>
 
-        DPM-Solver is designed to discretize an integral of the noise prediction model, and DPM-Solver++ is designed to
-        discretize an integral of the data prediction model. So we need to first convert the model output to the
-        corresponding type to match the algorithm.
+        The algorithm and model type are decoupled. You can use either DPMSolver or DPMSolver++ for both noise
+        prediction and data prediction models.
 
-        Note that the algorithm type and the model type is decoupled. That is to say, we can use either DPM-Solver or
-        DPM-Solver++ for both noise prediction model and data prediction model.
+        </Tip>
 
         Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`int`): current discrete timestep in the diffusion chain.
+            model_output (`torch.FloatTensor`):
+                The direct output from the learned diffusion model.
+            timestep (`int`):
+                The current discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
+                A current instance of a sample created by the diffusion process.
 
         Returns:
-            `torch.FloatTensor`: the converted model output.
+            `torch.FloatTensor`:
+                The converted model output.
         """
 
         # DPM-Solver++ needs to solve an integral of the data prediction model.
@@ -437,19 +429,21 @@ class DPMSolverMultistepInverseScheduler(SchedulerMixin, ConfigMixin):
         noise: Optional[torch.FloatTensor] = None,
     ) -> torch.FloatTensor:
         """
-        One step for the first-order DPM-Solver (equivalent to DDIM).
-
-        See https://arxiv.org/abs/2206.00927 for the detailed derivation.
+        One step for the first-order DPMSolver (equivalent to DDIM).
 
         Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`int`): current discrete timestep in the diffusion chain.
-            prev_timestep (`int`): previous discrete timestep in the diffusion chain.
+            model_output (`torch.FloatTensor`):
+                The direct output from the learned diffusion model.
+            timestep (`int`):
+                The current discrete timestep in the diffusion chain.
+            prev_timestep (`int`):
+                The previous discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
+                A current instance of a sample created by the diffusion process.
 
         Returns:
-            `torch.FloatTensor`: the sample tensor at the previous timestep.
+            `torch.FloatTensor`:
+                The sample tensor at the previous timestep.
         """
         lambda_t, lambda_s = self.lambda_t[prev_timestep], self.lambda_t[timestep]
         alpha_t, alpha_s = self.alpha_t[prev_timestep], self.alpha_t[timestep]
@@ -474,18 +468,21 @@ class DPMSolverMultistepInverseScheduler(SchedulerMixin, ConfigMixin):
         noise: Optional[torch.FloatTensor] = None,
     ) -> torch.FloatTensor:
         """
-        One step for the second-order multistep DPM-Solver.
+        One step for the second-order multistep DPMSolver.
 
         Args:
             model_output_list (`List[torch.FloatTensor]`):
-                direct outputs from learned diffusion model at current and latter timesteps.
-            timestep (`int`): current and latter discrete timestep in the diffusion chain.
-            prev_timestep (`int`): previous discrete timestep in the diffusion chain.
+                The direct outputs from learned diffusion model at current and latter timesteps.
+            timestep (`int`):
+                The current and latter discrete timestep in the diffusion chain.
+            prev_timestep (`int`):
+                The previous discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
+                A current instance of a sample created by the diffusion process.
 
         Returns:
-            `torch.FloatTensor`: the sample tensor at the previous timestep.
+            `torch.FloatTensor`:
+                The sample tensor at the previous timestep.
         """
         t, s0, s1 = prev_timestep, timestep_list[-1], timestep_list[-2]
         m0, m1 = model_output_list[-1], model_output_list[-2]
@@ -538,18 +535,21 @@ class DPMSolverMultistepInverseScheduler(SchedulerMixin, ConfigMixin):
         sample: torch.FloatTensor,
     ) -> torch.FloatTensor:
         """
-        One step for the third-order multistep DPM-Solver.
+        One step for the third-order multistep DPMSolver.
 
         Args:
             model_output_list (`List[torch.FloatTensor]`):
-                direct outputs from learned diffusion model at current and latter timesteps.
-            timestep (`int`): current and latter discrete timestep in the diffusion chain.
-            prev_timestep (`int`): previous discrete timestep in the diffusion chain.
+                The direct outputs from learned diffusion model at current and latter timesteps.
+            timestep (`int`):
+                The current and latter discrete timestep in the diffusion chain.
+            prev_timestep (`int`):
+                The previous discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
+                A current instance of a sample created by diffusion process.
 
         Returns:
-            `torch.FloatTensor`: the sample tensor at the previous timestep.
+            `torch.FloatTensor`:
+                The sample tensor at the previous timestep.
         """
         t, s0, s1, s2 = prev_timestep, timestep_list[-1], timestep_list[-2], timestep_list[-3]
         m0, m1, m2 = model_output_list[-1], model_output_list[-2], model_output_list[-3]
@@ -594,18 +594,23 @@ class DPMSolverMultistepInverseScheduler(SchedulerMixin, ConfigMixin):
         return_dict: bool = True,
     ) -> Union[SchedulerOutput, Tuple]:
         """
-        Step function propagating the sample with the multistep DPM-Solver.
+        Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
+        the multistep DPMSolver.
 
         Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`int`): current discrete timestep in the diffusion chain.
+            model_output (`torch.FloatTensor`):
+                The direct output from learned diffusion model.
+            timestep (`int`):
+                The current discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
-            return_dict (`bool`): option for returning tuple rather than SchedulerOutput class
+                A current instance of a sample created by the diffusion process.
+            return_dict (`bool`):
+                Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`.
 
         Returns:
-            [`~scheduling_utils.SchedulerOutput`] or `tuple`: [`~scheduling_utils.SchedulerOutput`] if `return_dict` is
-            True, otherwise a `tuple`. When returning a tuple, the first element is the sample tensor.
+            [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
+                If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a
+                tuple is returned where the first element is the sample tensor.
 
         """
         if self.num_inference_steps is None:
@@ -672,10 +677,12 @@ class DPMSolverMultistepInverseScheduler(SchedulerMixin, ConfigMixin):
         current timestep.
 
         Args:
-            sample (`torch.FloatTensor`): input sample
+            sample (`torch.FloatTensor`):
+                The input sample.
 
         Returns:
-            `torch.FloatTensor`: scaled input sample
+            `torch.FloatTensor`:
+                A scaled input sample.
         """
         return sample
 

src/diffusers/schedulers/scheduling_dpmsolver_sde.py

@@ -123,39 +123,40 @@ def betas_for_alpha_bar(
 
 class DPMSolverSDEScheduler(SchedulerMixin, ConfigMixin):
     """
-    Implements Stochastic Sampler (Algorithm 2) from Karras et al. (2022). Based on the original k-diffusion
-    implementation by Katherine Crowson:
-    https://github.com/crowsonkb/k-diffusion/blob/41b4cb6df0506694a7776af31349acf082bf6091/k_diffusion/sampling.py#L543
+    DPMSolverSDEScheduler implements the stochastic sampler from the [Elucidating the Design Space of Diffusion-Based
+    Generative Models](https://huggingface.co/papers/2206.00364) paper.
 
-    [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
-    function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`.
-    [`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and
-    [`~SchedulerMixin.from_pretrained`] functions.
+    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
+    methods the library implements for all schedulers such as loading and saving.
 
     Args:
-        num_train_timesteps (`int`): number of diffusion steps used to train the model. beta_start (`float`): the
-        starting `beta` value of inference. beta_end (`float`): the final `beta` value. beta_schedule (`str`):
-            the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
+        num_train_timesteps (`int`, defaults to 1000):
+            The number of diffusion steps to train the model.
+        beta_start (`float`, defaults to 0.00085):
+            The starting `beta` value of inference.
+        beta_end (`float`, defaults to 0.012):
+            The final `beta` value.
+        beta_schedule (`str`, defaults to `"linear"`):
+            The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
             `linear` or `scaled_linear`.
-        trained_betas (`np.ndarray`, optional):
-            option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
-        prediction_type (`str`, default `epsilon`, optional):
-            prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion
-            process), `sample` (directly predicting the noisy sample`) or `v_prediction` (see section 2.4
-            https://imagen.research.google/video/paper.pdf)
+        trained_betas (`np.ndarray`, *optional*):
+            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
+        prediction_type (`str`, defaults to `epsilon`, *optional*):
+            Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
+            `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen
+            Video](https://imagen.research.google/video/paper.pdf) paper).
         use_karras_sigmas (`bool`, *optional*, defaults to `False`):
-             This parameter controls whether to use Karras sigmas (Karras et al. (2022) scheme) for step sizes in the
-             noise schedule during the sampling process. If True, the sigmas will be determined according to a sequence
-             of noise levels {σi} as defined in Equation (5) of the paper https://arxiv.org/pdf/2206.00364.pdf.
+            Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. If `True`,
+            the sigmas are determined according to a sequence of noise levels {σi}.
         noise_sampler_seed (`int`, *optional*, defaults to `None`):
-            The random seed to use for the noise sampler. If `None`, a random seed will be generated.
-        timestep_spacing (`str`, default `"linspace"`):
-            The way the timesteps should be scaled. Refer to Table 2. of [Common Diffusion Noise Schedules and Sample
-            Steps are Flawed](https://arxiv.org/abs/2305.08891) for more information.
-        steps_offset (`int`, default `0`):
-            an offset added to the inference steps. You can use a combination of `offset=1` and
-            `set_alpha_to_one=False`, to make the last step use step 0 for the previous alpha product, as done in
-            stable diffusion.
+            The random seed to use for the noise sampler. If `None`, a random seed is generated.
+        timestep_spacing (`str`, defaults to `"linspace"`):
+            The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
+            Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
+        steps_offset (`int`, defaults to 0):
+            An offset added to the inference steps. You can use a combination of `offset=1` and
+            `set_alpha_to_one=False` to make the last step use step 0 for the previous alpha product like in Stable
+            Diffusion.
     """
 
     _compatibles = [e.name for e in KarrasDiffusionSchedulers]
@@ -232,12 +233,18 @@ class DPMSolverSDEScheduler(SchedulerMixin, ConfigMixin):
         timestep: Union[float, torch.FloatTensor],
     ) -> torch.FloatTensor:
         """
-        Args:
         Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
         current timestep.
-            sample (`torch.FloatTensor`): input sample timestep (`int`, optional): current timestep
+
+        Args:
+            sample (`torch.FloatTensor`):
+                The input sample.
+            timestep (`int`, *optional*):
+                The current timestep in the diffusion chain.
+
         Returns:
-            `torch.FloatTensor`: scaled input sample
+            `torch.FloatTensor`:
+                A scaled input sample.
         """
         step_index = self.index_for_timestep(timestep)
 
@@ -253,13 +260,13 @@ class DPMSolverSDEScheduler(SchedulerMixin, ConfigMixin):
         num_train_timesteps: Optional[int] = None,
     ):
         """
-        Sets the timesteps used for the diffusion chain. Supporting function to be run before inference.
+        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
 
         Args:
             num_inference_steps (`int`):
-                the number of diffusion steps used when generating samples with a pre-trained model.
-            device (`str` or `torch.device`, optional):
-                the device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
+                The number of diffusion steps used when generating samples with a pre-trained model.
+            device (`str` or `torch.device`, *optional*):
+                The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
         """
         self.num_inference_steps = num_inference_steps
 
@@ -384,18 +391,25 @@ class DPMSolverSDEScheduler(SchedulerMixin, ConfigMixin):
         s_noise: float = 1.0,
     ) -> Union[SchedulerOutput, Tuple]:
         """
-        Args:
-        Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
+        Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
         process from the learned model outputs (most often the predicted noise).
-        model_output (Union[torch.FloatTensor, np.ndarray]): Direct output from learned diffusion model.
-        timestep (Union[float, torch.FloatTensor]): Current discrete timestep in the diffusion chain.
-        sample (Union[torch.FloatTensor, np.ndarray]): Current instance of sample being created by diffusion process.
-        return_dict (bool, optional): Option for returning tuple rather than SchedulerOutput class. Defaults to True.
-        s_noise (float, optional): Scaling factor for the noise added to the sample. Defaults to 1.0.
+
+        Args:
+            model_output (`torch.FloatTensor` or `np.ndarray`):
+                The direct output from learned diffusion model.
+            timestep (`float` or `torch.FloatTensor`):
+                The current discrete timestep in the diffusion chain.
+            sample (`torch.FloatTensor` or `np.ndarray`):
+                A current instance of a sample created by the diffusion process.
+            return_dict (`bool`, *optional*, defaults to `True`):
+                Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or tuple.
+            s_noise (`float`, *optional*, defaults to 1.0):
+                Scaling factor for noise added to the sample.
+
         Returns:
             [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
-            [`~schedulers.scheduling_utils.SchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When
-            returning a tuple, the first element is the sample tensor.
+                If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a
+                tuple is returned where the first element is the sample tensor.
         """
         step_index = self.index_for_timestep(timestep)
 

src/diffusers/schedulers/scheduling_dpmsolver_singlestep.py

@@ -75,79 +75,59 @@ def betas_for_alpha_bar(
 
 class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
     """
-    DPM-Solver (and the improved version DPM-Solver++) is a fast dedicated high-order solver for diffusion ODEs with
-    the convergence order guarantee. Empirically, sampling by DPM-Solver with only 20 steps can generate high-quality
-    samples, and it can generate quite good samples even in only 10 steps.
+    `DPMSolverSinglestepScheduler` is a fast dedicated high-order solver for diffusion ODEs.
 
-    For more details, see the original paper: https://arxiv.org/abs/2206.00927 and https://arxiv.org/abs/2211.01095
-
-    Currently, we support the singlestep DPM-Solver for both noise prediction models and data prediction models. We
-    recommend to use `solver_order=2` for guided sampling, and `solver_order=3` for unconditional sampling.
-
-    We also support the "dynamic thresholding" method in Imagen (https://arxiv.org/abs/2205.11487). For pixel-space
-    diffusion models, you can set both `algorithm_type="dpmsolver++"` and `thresholding=True` to use the dynamic
-    thresholding. Note that the thresholding method is unsuitable for latent-space diffusion models (such as
-    stable-diffusion).
-
-    [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
-    function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`.
-    [`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and
-    [`~SchedulerMixin.from_pretrained`] functions.
+    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
+    methods the library implements for all schedulers such as loading and saving.
 
     Args:
-        num_train_timesteps (`int`): number of diffusion steps used to train the model.
-        beta_start (`float`): the starting `beta` value of inference.
-        beta_end (`float`): the final `beta` value.
-        beta_schedule (`str`):
-            the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
+        num_train_timesteps (`int`, defaults to 1000):
+            The number of diffusion steps to train the model.
+        beta_start (`float`, defaults to 0.0001):
+            The starting `beta` value of inference.
+        beta_end (`float`, defaults to 0.02):
+            The final `beta` value.
+        beta_schedule (`str`, defaults to `"linear"`):
+            The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
             `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
-        trained_betas (`np.ndarray`, optional):
-            option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
-        solver_order (`int`, default `2`):
-            the order of DPM-Solver; can be `1` or `2` or `3`. We recommend to use `solver_order=2` for guided
+        trained_betas (`np.ndarray`, *optional*):
+            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
+        solver_order (`int`, defaults to 2):
+            The DPMSolver order which can be `1` or `2` or `3`. It is recommended to use `solver_order=2` for guided
             sampling, and `solver_order=3` for unconditional sampling.
-        prediction_type (`str`, default `epsilon`):
-            indicates whether the model predicts the noise (epsilon), or the data / `x0`. One of `epsilon`, `sample`,
-            or `v-prediction`.
-        thresholding (`bool`, default `False`):
-            whether to use the "dynamic thresholding" method (introduced by Imagen, https://arxiv.org/abs/2205.11487).
-            For pixel-space diffusion models, you can set both `algorithm_type=dpmsolver++` and `thresholding=True` to
-            use the dynamic thresholding. Note that the thresholding method is unsuitable for latent-space diffusion
-            models (such as stable-diffusion).
-        dynamic_thresholding_ratio (`float`, default `0.995`):
-            the ratio for the dynamic thresholding method. Default is `0.995`, the same as Imagen
-            (https://arxiv.org/abs/2205.11487).
-        sample_max_value (`float`, default `1.0`):
-            the threshold value for dynamic thresholding. Valid only when `thresholding=True` and
-            `algorithm_type="dpmsolver++`.
-        algorithm_type (`str`, default `dpmsolver++`):
-            the algorithm type for the solver. Either `dpmsolver` or `dpmsolver++`. The `dpmsolver` type implements the
-            algorithms in https://arxiv.org/abs/2206.00927, and the `dpmsolver++` type implements the algorithms in
-            https://arxiv.org/abs/2211.01095. We recommend to use `dpmsolver++` with `solver_order=2` for guided
-            sampling (e.g. stable-diffusion).
-        solver_type (`str`, default `midpoint`):
-            the solver type for the second-order solver. Either `midpoint` or `heun`. The solver type slightly affects
-            the sample quality, especially for small number of steps. We empirically find that `midpoint` solvers are
-            slightly better, so we recommend to use the `midpoint` type.
-        lower_order_final (`bool`, default `True`):
-            whether to use lower-order solvers in the final steps. For singlestep schedulers, we recommend to enable
-            this to use up all the function evaluations.
+        prediction_type (`str`, defaults to `epsilon`, *optional*):
+            Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
+            `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen
+            Video](https://imagen.research.google/video/paper.pdf) paper).
+        thresholding (`bool`, defaults to `False`):
+            Whether to use the "dynamic thresholding" method. This is unsuitable for latent-space diffusion models such
+            as Stable Diffusion.
+        dynamic_thresholding_ratio (`float`, defaults to 0.995):
+            The ratio for the dynamic thresholding method. Valid only when `thresholding=True`.
+        sample_max_value (`float`, defaults to 1.0):
+            The threshold value for dynamic thresholding. Valid only when `thresholding=True` and
+            `algorithm_type="dpmsolver++"`.
+        algorithm_type (`str`, defaults to `dpmsolver++`):
+            Algorithm type for the solver; can be `dpmsolver`, `dpmsolver++`, `sde-dpmsolver` or `sde-dpmsolver++`. The
+            `dpmsolver` type implements the algorithms in the [DPMSolver](https://huggingface.co/papers/2206.00927)
+            paper, and the `dpmsolver++` type implements the algorithms in the
+            [DPMSolver++](https://huggingface.co/papers/2211.01095) paper. It is recommended to use `dpmsolver++` or
+            `sde-dpmsolver++` with `solver_order=2` for guided sampling like in Stable Diffusion.
+        solver_type (`str`, defaults to `midpoint`):
+            Solver type for the second-order solver; can be `midpoint` or `heun`. The solver type slightly affects the
+            sample quality, especially for a small number of steps. It is recommended to use `midpoint` solvers.
+        lower_order_final (`bool`, defaults to `True`):
+            Whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. This can
+            stabilize the sampling of DPMSolver for steps < 15, especially for steps <= 10.
         use_karras_sigmas (`bool`, *optional*, defaults to `False`):
-             This parameter controls whether to use Karras sigmas (Karras et al. (2022) scheme) for step sizes in the
-             noise schedule during the sampling process. If True, the sigmas will be determined according to a sequence
-             of noise levels {σi} as defined in Equation (5) of the paper https://arxiv.org/pdf/2206.00364.pdf.
-        lambda_min_clipped (`float`, default `-inf`):
-            the clipping threshold for the minimum value of lambda(t) for numerical stability. This is critical for
-            cosine (squaredcos_cap_v2) noise schedule.
+            Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. If `True`,
+            the sigmas are determined according to a sequence of noise levels {σi}.
+        lambda_min_clipped (`float`, defaults to `-inf`):
+            Clipping threshold for the minimum value of `lambda(t)` for numerical stability. This is critical for the
+            cosine (`squaredcos_cap_v2`) noise schedule.
         variance_type (`str`, *optional*):
-            Set to "learned" or "learned_range" for diffusion models that predict variance. For example, OpenAI's
-            guided-diffusion (https://github.com/openai/guided-diffusion) predicts both mean and variance of the
-            Gaussian distribution in the model's output. DPM-Solver only needs the "mean" output because it is based on
-            diffusion ODEs. whether the model's output contains the predicted Gaussian variance. For example, OpenAI's
-            guided-diffusion (https://github.com/openai/guided-diffusion) predicts both mean and variance of the
-            Gaussian distribution in the model's output. DPM-Solver only needs the "mean" output because it is based on
-            diffusion ODEs.
-
+            Set to "learned" or "learned_range" for diffusion models that predict variance. If set, the model's output
+            contains the predicted Gaussian variance.
     """
 
     _compatibles = [e.name for e in KarrasDiffusionSchedulers]
@@ -224,7 +204,7 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
 
         Args:
             num_inference_steps (`int`):
-                the number of diffusion steps used when generating samples with a pre-trained model.
+                The number of diffusion steps used when generating samples with a pre-trained model.
         """
         steps = num_inference_steps
         order = self.config.solver_order
@@ -254,13 +234,13 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
 
     def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
         """
-        Sets the timesteps used for the diffusion chain. Supporting function to be run before inference.
+        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
 
         Args:
             num_inference_steps (`int`):
-                the number of diffusion steps used when generating samples with a pre-trained model.
-            device (`str` or `torch.device`, optional):
-                the device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
+                The number of diffusion steps used when generating samples with a pre-trained model.
+            device (`str` or `torch.device`, *optional*):
+                The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
         """
         self.num_inference_steps = num_inference_steps
         # Clipping the minimum of all lambda(t) for numerical stability.
@@ -371,23 +351,28 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
         self, model_output: torch.FloatTensor, timestep: int, sample: torch.FloatTensor
     ) -> torch.FloatTensor:
         """
-        Convert the model output to the corresponding type that the algorithm (DPM-Solver / DPM-Solver++) needs.
+        Convert the model output to the corresponding type the DPMSolver/DPMSolver++ algorithm needs. DPM-Solver is
+        designed to discretize an integral of the noise prediction model, and DPM-Solver++ is designed to discretize an
+        integral of the data prediction model.
+
+        <Tip>
 
-        DPM-Solver is designed to discretize an integral of the noise prediction model, and DPM-Solver++ is designed to
-        discretize an integral of the data prediction model. So we need to first convert the model output to the
-        corresponding type to match the algorithm.
+        The algorithm and model type are decoupled. You can use either DPMSolver or DPMSolver++ for both noise
+        prediction and data prediction models.
 
-        Note that the algorithm type and the model type is decoupled. That is to say, we can use either DPM-Solver or
-        DPM-Solver++ for both noise prediction model and data prediction model.
+        </Tip>
 
         Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`int`): current discrete timestep in the diffusion chain.
+            model_output (`torch.FloatTensor`):
+                The direct output from the learned diffusion model.
+            timestep (`int`):
+                The current discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
+                A current instance of a sample created by the diffusion process.
 
         Returns:
-            `torch.FloatTensor`: the converted model output.
+            `torch.FloatTensor`:
+                The converted model output.
         """
         # DPM-Solver++ needs to solve an integral of the data prediction model.
         if self.config.algorithm_type == "dpmsolver++":
@@ -441,19 +426,21 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
         sample: torch.FloatTensor,
     ) -> torch.FloatTensor:
         """
-        One step for the first-order DPM-Solver (equivalent to DDIM).
-
-        See https://arxiv.org/abs/2206.00927 for the detailed derivation.
+        One step for the first-order DPMSolver (equivalent to DDIM).
 
         Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`int`): current discrete timestep in the diffusion chain.
-            prev_timestep (`int`): previous discrete timestep in the diffusion chain.
+            model_output (`torch.FloatTensor`):
+                The direct output from the learned diffusion model.
+            timestep (`int`):
+                The current discrete timestep in the diffusion chain.
+            prev_timestep (`int`):
+                The previous discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
+                A current instance of a sample created by the diffusion process.
 
         Returns:
-            `torch.FloatTensor`: the sample tensor at the previous timestep.
+            `torch.FloatTensor`:
+                The sample tensor at the previous timestep.
         """
         lambda_t, lambda_s = self.lambda_t[prev_timestep], self.lambda_t[timestep]
         alpha_t, alpha_s = self.alpha_t[prev_timestep], self.alpha_t[timestep]
@@ -473,20 +460,22 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
         sample: torch.FloatTensor,
     ) -> torch.FloatTensor:
         """
-        One step for the second-order singlestep DPM-Solver.
-
-        It computes the solution at time `prev_timestep` from the time `timestep_list[-2]`.
+        One step for the second-order singlestep DPMSolver that computes the solution at time `prev_timestep` from the
+        time `timestep_list[-2]`.
 
         Args:
             model_output_list (`List[torch.FloatTensor]`):
-                direct outputs from learned diffusion model at current and latter timesteps.
-            timestep (`int`): current and latter discrete timestep in the diffusion chain.
-            prev_timestep (`int`): previous discrete timestep in the diffusion chain.
+                The direct outputs from learned diffusion model at current and latter timesteps.
+            timestep (`int`):
+                The current and latter discrete timestep in the diffusion chain.
+            prev_timestep (`int`):
+                The previous discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
+                A current instance of a sample created by the diffusion process.
 
         Returns:
-            `torch.FloatTensor`: the sample tensor at the previous timestep.
+            `torch.FloatTensor`:
+                The sample tensor at the previous timestep.
         """
         t, s0, s1 = prev_timestep, timestep_list[-1], timestep_list[-2]
         m0, m1 = model_output_list[-1], model_output_list[-2]
@@ -534,20 +523,22 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
         sample: torch.FloatTensor,
     ) -> torch.FloatTensor:
         """
-        One step for the third-order singlestep DPM-Solver.
-
-        It computes the solution at time `prev_timestep` from the time `timestep_list[-3]`.
+        One step for the third-order singlestep DPMSolver that computes the solution at time `prev_timestep` from the
+        time `timestep_list[-3]`.
 
         Args:
             model_output_list (`List[torch.FloatTensor]`):
-                direct outputs from learned diffusion model at current and latter timesteps.
-            timestep (`int`): current and latter discrete timestep in the diffusion chain.
-            prev_timestep (`int`): previous discrete timestep in the diffusion chain.
+                The direct outputs from learned diffusion model at current and latter timesteps.
+            timestep (`int`):
+                The current and latter discrete timestep in the diffusion chain.
+            prev_timestep (`int`):
+                The previous discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
+                A current instance of a sample created by diffusion process.
 
         Returns:
-            `torch.FloatTensor`: the sample tensor at the previous timestep.
+            `torch.FloatTensor`:
+                The sample tensor at the previous timestep.
         """
         t, s0, s1, s2 = prev_timestep, timestep_list[-1], timestep_list[-2], timestep_list[-3]
         m0, m1, m2 = model_output_list[-1], model_output_list[-2], model_output_list[-3]
@@ -606,20 +597,23 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
         order: int,
     ) -> torch.FloatTensor:
         """
-        One step for the singlestep DPM-Solver.
+        One step for the singlestep DPMSolver.
 
         Args:
             model_output_list (`List[torch.FloatTensor]`):
-                direct outputs from learned diffusion model at current and latter timesteps.
-            timestep (`int`): current and latter discrete timestep in the diffusion chain.
-            prev_timestep (`int`): previous discrete timestep in the diffusion chain.
+                The direct outputs from learned diffusion model at current and latter timesteps.
+            timestep (`int`):
+                The current and latter discrete timestep in the diffusion chain.
+            prev_timestep (`int`):
+                The previous discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
+                A current instance of a sample created by diffusion process.
             order (`int`):
-                the solver order at this step.
+                The solver order at this step.
 
         Returns:
-            `torch.FloatTensor`: the sample tensor at the previous timestep.
+            `torch.FloatTensor`:
+                The sample tensor at the previous timestep.
         """
         if order == 1:
             return self.dpm_solver_first_order_update(model_output_list[-1], timestep_list[-1], prev_timestep, sample)
@@ -642,18 +636,23 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
         return_dict: bool = True,
     ) -> Union[SchedulerOutput, Tuple]:
         """
-        Step function propagating the sample with the singlestep DPM-Solver.
+        Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
+        the singlestep DPMSolver.
 
         Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`int`): current discrete timestep in the diffusion chain.
+            model_output (`torch.FloatTensor`):
+                The direct output from learned diffusion model.
+            timestep (`int`):
+                The current discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
-            return_dict (`bool`): option for returning tuple rather than SchedulerOutput class
+                A current instance of a sample created by the diffusion process.
+            return_dict (`bool`):
+                Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`.
 
         Returns:
-            [`~scheduling_utils.SchedulerOutput`] or `tuple`: [`~scheduling_utils.SchedulerOutput`] if `return_dict` is
-            True, otherwise a `tuple`. When returning a tuple, the first element is the sample tensor.
+            [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
+                If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a
+                tuple is returned where the first element is the sample tensor.
 
         """
         if self.num_inference_steps is None:
@@ -702,10 +701,12 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
         current timestep.
 
         Args:
-            sample (`torch.FloatTensor`): input sample
+            sample (`torch.FloatTensor`):
+                The input sample.
 
         Returns:
-            `torch.FloatTensor`: scaled input sample
+            `torch.FloatTensor`:
+                A scaled input sample.
         """
         return sample
 

src/diffusers/schedulers/scheduling_euler_ancestral_discrete.py

@@ -31,14 +31,14 @@ logger = logging.get_logger(__name__)  # pylint: disable=invalid-name
 # Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerAncestralDiscrete
 class EulerAncestralDiscreteSchedulerOutput(BaseOutput):
     """
-    Output class for the scheduler's step function output.
+    Output class for the scheduler's `step` function output.
 
     Args:
         prev_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
-            Computed sample (x_{t-1}) of previous timestep. `prev_sample` should be used as next model input in the
+            Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the
             denoising loop.
         pred_original_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
-            The predicted denoised sample (x_{0}) based on the model output from the current timestep.
+            The predicted denoised sample `(x_{0})` based on the model output from the current timestep.
             `pred_original_sample` can be used to preview progress or for guidance.
     """
 
@@ -93,34 +93,34 @@ def betas_for_alpha_bar(
 
 class EulerAncestralDiscreteScheduler(SchedulerMixin, ConfigMixin):
     """
-    Ancestral sampling with Euler method steps. Based on the original k-diffusion implementation by Katherine Crowson:
-    https://github.com/crowsonkb/k-diffusion/blob/481677d114f6ea445aa009cf5bd7a9cdee909e47/k_diffusion/sampling.py#L72
+    Ancestral sampling with Euler method steps.
 
-    [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
-    function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`.
-    [`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and
-    [`~SchedulerMixin.from_pretrained`] functions.
+    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
+    methods the library implements for all schedulers such as loading and saving.
 
     Args:
-        num_train_timesteps (`int`): number of diffusion steps used to train the model.
-        beta_start (`float`): the starting `beta` value of inference.
-        beta_end (`float`): the final `beta` value.
-        beta_schedule (`str`):
-            the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
+        num_train_timesteps (`int`, defaults to 1000):
+            The number of diffusion steps to train the model.
+        beta_start (`float`, defaults to 0.0001):
+            The starting `beta` value of inference.
+        beta_end (`float`, defaults to 0.02):
+            The final `beta` value.
+        beta_schedule (`str`, defaults to `"linear"`):
+            The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
             `linear` or `scaled_linear`.
-        trained_betas (`np.ndarray`, optional):
-            option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
-        prediction_type (`str`, default `epsilon`, optional):
-            prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion
-            process), `sample` (directly predicting the noisy sample`) or `v_prediction` (see section 2.4
-            https://imagen.research.google/video/paper.pdf)
-        timestep_spacing (`str`, default `"linspace"`):
-            The way the timesteps should be scaled. Refer to Table 2. of [Common Diffusion Noise Schedules and Sample
-            Steps are Flawed](https://arxiv.org/abs/2305.08891) for more information.
-        steps_offset (`int`, default `0`):
-            an offset added to the inference steps. You can use a combination of `offset=1` and
-            `set_alpha_to_one=False`, to make the last step use step 0 for the previous alpha product, as done in
-            stable diffusion.
+        trained_betas (`np.ndarray`, *optional*):
+            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
+        prediction_type (`str`, defaults to `epsilon`, *optional*):
+            Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
+            `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen
+            Video](https://imagen.research.google/video/paper.pdf) paper).
+        timestep_spacing (`str`, defaults to `"linspace"`):
+            The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
+            Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
+        steps_offset (`int`, defaults to 0):
+            An offset added to the inference steps. You can use a combination of `offset=1` and
+            `set_alpha_to_one=False` to make the last step use step 0 for the previous alpha product like in Stable
+            Diffusion.
     """
 
     _compatibles = [e.name for e in KarrasDiffusionSchedulers]
@@ -178,14 +178,18 @@ class EulerAncestralDiscreteScheduler(SchedulerMixin, ConfigMixin):
         self, sample: torch.FloatTensor, timestep: Union[float, torch.FloatTensor]
     ) -> torch.FloatTensor:
         """
-        Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the Euler algorithm.
+        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
+        current timestep. Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the Euler algorithm.
 
         Args:
-            sample (`torch.FloatTensor`): input sample
-            timestep (`float` or `torch.FloatTensor`): the current timestep in the diffusion chain
+            sample (`torch.FloatTensor`):
+                The input sample.
+            timestep (`int`, *optional*):
+                The current timestep in the diffusion chain.
 
         Returns:
-            `torch.FloatTensor`: scaled input sample
+            `torch.FloatTensor`:
+                A scaled input sample.
         """
         if isinstance(timestep, torch.Tensor):
             timestep = timestep.to(self.timesteps.device)
@@ -197,13 +201,13 @@ class EulerAncestralDiscreteScheduler(SchedulerMixin, ConfigMixin):
 
     def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
         """
-        Sets the timesteps used for the diffusion chain. Supporting function to be run before inference.
+        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
 
         Args:
             num_inference_steps (`int`):
-                the number of diffusion steps used when generating samples with a pre-trained model.
-            device (`str` or `torch.device`, optional):
-                the device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
+                The number of diffusion steps used when generating samples with a pre-trained model.
+            device (`str` or `torch.device`, *optional*):
+                The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
         """
         self.num_inference_steps = num_inference_steps
 
@@ -248,21 +252,27 @@ class EulerAncestralDiscreteScheduler(SchedulerMixin, ConfigMixin):
         return_dict: bool = True,
     ) -> Union[EulerAncestralDiscreteSchedulerOutput, Tuple]:
         """
-        Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
+        Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
         process from the learned model outputs (most often the predicted noise).
 
         Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`float`): current timestep in the diffusion chain.
+            model_output (`torch.FloatTensor`):
+                The direct output from learned diffusion model.
+            timestep (`float`):
+                The current discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
-            generator (`torch.Generator`, optional): Random number generator.
-            return_dict (`bool`): option for returning tuple rather than EulerAncestralDiscreteSchedulerOutput class
+                A current instance of a sample created by the diffusion process.
+            generator (`torch.Generator`, *optional*):
+                A random number generator.
+            return_dict (`bool`):
+                Whether or not to return a
+                [`~schedulers.scheduling_euler_ancestral_discrete.EulerAncestralDiscreteSchedulerOutput`] or tuple.
 
         Returns:
-            [`~schedulers.scheduling_utils.EulerAncestralDiscreteSchedulerOutput`] or `tuple`:
-            [`~schedulers.scheduling_utils.EulerAncestralDiscreteSchedulerOutput`] if `return_dict` is True, otherwise
-            a `tuple`. When returning a tuple, the first element is the sample tensor.
+            [`~schedulers.scheduling_euler_ancestral_discrete.EulerAncestralDiscreteSchedulerOutput`] or `tuple`:
+                If return_dict is `True`,
+                [`~schedulers.scheduling_euler_ancestral_discrete.EulerAncestralDiscreteSchedulerOutput`] is returned,
+                otherwise a tuple is returned where the first element is the sample tensor.
 
         """
 

src/diffusers/schedulers/scheduling_euler_discrete.py

@@ -31,14 +31,14 @@ logger = logging.get_logger(__name__)  # pylint: disable=invalid-name
 # Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
 class EulerDiscreteSchedulerOutput(BaseOutput):
     """
-    Output class for the scheduler's step function output.
+    Output class for the scheduler's `step` function output.
 
     Args:
         prev_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
-            Computed sample (x_{t-1}) of previous timestep. `prev_sample` should be used as next model input in the
+            Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the
             denoising loop.
         pred_original_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
-            The predicted denoised sample (x_{0}) based on the model output from the current timestep.
+            The predicted denoised sample `(x_{0})` based on the model output from the current timestep.
             `pred_original_sample` can be used to preview progress or for guidance.
     """
 
@@ -93,42 +93,40 @@ def betas_for_alpha_bar(
 
 class EulerDiscreteScheduler(SchedulerMixin, ConfigMixin):
     """
-    Euler scheduler (Algorithm 2) from Karras et al. (2022) https://arxiv.org/abs/2206.00364. . Based on the original
-    k-diffusion implementation by Katherine Crowson:
-    https://github.com/crowsonkb/k-diffusion/blob/481677d114f6ea445aa009cf5bd7a9cdee909e47/k_diffusion/sampling.py#L51
+    Euler scheduler.
 
-    [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
-    function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`.
-    [`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and
-    [`~SchedulerMixin.from_pretrained`] functions.
+    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
+    methods the library implements for all schedulers such as loading and saving.
 
     Args:
-        num_train_timesteps (`int`): number of diffusion steps used to train the model.
-        beta_start (`float`): the starting `beta` value of inference.
-        beta_end (`float`): the final `beta` value.
-        beta_schedule (`str`):
-            the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
+        num_train_timesteps (`int`, defaults to 1000):
+            The number of diffusion steps to train the model.
+        beta_start (`float`, defaults to 0.0001):
+            The starting `beta` value of inference.
+        beta_end (`float`, defaults to 0.02):
+            The final `beta` value.
+        beta_schedule (`str`, defaults to `"linear"`):
+            The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
             `linear` or `scaled_linear`.
-        trained_betas (`np.ndarray`, optional):
-            option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
-        prediction_type (`str`, default `"epsilon"`, optional):
-            prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion
-            process), `sample` (directly predicting the noisy sample`) or `v_prediction` (see section 2.4
-            https://imagen.research.google/video/paper.pdf)
-        interpolation_type (`str`, default `"linear"`, optional):
-            interpolation type to compute intermediate sigmas for the scheduler denoising steps. Should be one of
-            [`"linear"`, `"log_linear"`].
+        trained_betas (`np.ndarray`, *optional*):
+            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
+        prediction_type (`str`, defaults to `epsilon`, *optional*):
+            Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
+            `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen
+            Video](https://imagen.research.google/video/paper.pdf) paper).
+        interpolation_type(`str`, defaults to `"linear"`, *optional*):
+            The interpolation type to compute intermediate sigmas for the scheduler denoising steps. Should be on of
+            `"linear"` or `"log_linear"`.
         use_karras_sigmas (`bool`, *optional*, defaults to `False`):
-             This parameter controls whether to use Karras sigmas (Karras et al. (2022) scheme) for step sizes in the
-             noise schedule during the sampling process. If True, the sigmas will be determined according to a sequence
-             of noise levels {σi} as defined in Equation (5) of the paper https://arxiv.org/pdf/2206.00364.pdf.
-        timestep_spacing (`str`, default `"linspace"`):
-            The way the timesteps should be scaled. Refer to Table 2. of [Common Diffusion Noise Schedules and Sample
-            Steps are Flawed](https://arxiv.org/abs/2305.08891) for more information.
-        steps_offset (`int`, default `0`):
-            an offset added to the inference steps. You can use a combination of `offset=1` and
-            `set_alpha_to_one=False`, to make the last step use step 0 for the previous alpha product, as done in
-            stable diffusion.
+            Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. If `True`,
+            the sigmas are determined according to a sequence of noise levels {σi}.
+        timestep_spacing (`str`, defaults to `"linspace"`):
+            The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
+            Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
+        steps_offset (`int`, defaults to 0):
+            An offset added to the inference steps. You can use a combination of `offset=1` and
+            `set_alpha_to_one=False` to make the last step use step 0 for the previous alpha product like in Stable
+            Diffusion.
     """
 
     _compatibles = [e.name for e in KarrasDiffusionSchedulers]
@@ -189,14 +187,18 @@ class EulerDiscreteScheduler(SchedulerMixin, ConfigMixin):
         self, sample: torch.FloatTensor, timestep: Union[float, torch.FloatTensor]
     ) -> torch.FloatTensor:
         """
-        Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the Euler algorithm.
+        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
+        current timestep. Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the Euler algorithm.
 
         Args:
-            sample (`torch.FloatTensor`): input sample
-            timestep (`float` or `torch.FloatTensor`): the current timestep in the diffusion chain
+            sample (`torch.FloatTensor`):
+                The input sample.
+            timestep (`int`, *optional*):
+                The current timestep in the diffusion chain.
 
         Returns:
-            `torch.FloatTensor`: scaled input sample
+            `torch.FloatTensor`:
+                A scaled input sample.
         """
         if isinstance(timestep, torch.Tensor):
             timestep = timestep.to(self.timesteps.device)
@@ -210,13 +212,13 @@ class EulerDiscreteScheduler(SchedulerMixin, ConfigMixin):
 
     def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
         """
-        Sets the timesteps used for the diffusion chain. Supporting function to be run before inference.
+        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
 
         Args:
             num_inference_steps (`int`):
-                the number of diffusion steps used when generating samples with a pre-trained model.
-            device (`str` or `torch.device`, optional):
-                the device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
+                The number of diffusion steps used when generating samples with a pre-trained model.
+            device (`str` or `torch.device`, *optional*):
+                The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
         """
         self.num_inference_steps = num_inference_steps
 
@@ -317,26 +319,31 @@ class EulerDiscreteScheduler(SchedulerMixin, ConfigMixin):
         return_dict: bool = True,
     ) -> Union[EulerDiscreteSchedulerOutput, Tuple]:
         """
-        Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
+        Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
         process from the learned model outputs (most often the predicted noise).
 
         Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`float`): current timestep in the diffusion chain.
+            model_output (`torch.FloatTensor`):
+                The direct output from learned diffusion model.
+            timestep (`float`):
+                The current discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
-            s_churn (`float`)
-            s_tmin  (`float`)
-            s_tmax  (`float`)
-            s_noise (`float`)
-            generator (`torch.Generator`, optional): Random number generator.
-            return_dict (`bool`): option for returning tuple rather than EulerDiscreteSchedulerOutput class
+                A current instance of a sample created by the diffusion process.
+            s_churn (`float`):
+            s_tmin  (`float`):
+            s_tmax  (`float`):
+            s_noise (`float`, defaults to 1.0):
+                Scaling factor for noise added to the sample.
+            generator (`torch.Generator`, *optional*):
+                A random number generator.
+            return_dict (`bool`):
+                Whether or not to return a [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] or
+                tuple.
 
         Returns:
-            [`~schedulers.scheduling_utils.EulerDiscreteSchedulerOutput`] or `tuple`:
-            [`~schedulers.scheduling_utils.EulerDiscreteSchedulerOutput`] if `return_dict` is True, otherwise a
-            `tuple`. When returning a tuple, the first element is the sample tensor.
-
+            [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] or `tuple`:
+                If return_dict is `True`, [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] is
+                returned, otherwise a tuple is returned where the first element is the sample tensor.
         """
 
         if (

src/diffusers/schedulers/scheduling_heun_discrete.py

@@ -70,41 +70,41 @@ def betas_for_alpha_bar(
 
 class HeunDiscreteScheduler(SchedulerMixin, ConfigMixin):
     """
-    Implements Algorithm 2 (Heun steps) from Karras et al. (2022). for discrete beta schedules. Based on the original
-    k-diffusion implementation by Katherine Crowson:
-    https://github.com/crowsonkb/k-diffusion/blob/481677d114f6ea445aa009cf5bd7a9cdee909e47/k_diffusion/sampling.py#L90
+    Scheduler with Heun steps for discrete beta schedules.
 
-    [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
-    function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`.
-    [`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and
-    [`~SchedulerMixin.from_pretrained`] functions.
+    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
+    methods the library implements for all schedulers such as loading and saving.
 
     Args:
-        num_train_timesteps (`int`): number of diffusion steps used to train the model. beta_start (`float`): the
-        starting `beta` value of inference. beta_end (`float`): the final `beta` value. beta_schedule (`str`):
-            the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
+        num_train_timesteps (`int`, defaults to 1000):
+            The number of diffusion steps to train the model.
+        beta_start (`float`, defaults to 0.0001):
+            The starting `beta` value of inference.
+        beta_end (`float`, defaults to 0.02):
+            The final `beta` value.
+        beta_schedule (`str`, defaults to `"linear"`):
+            The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
             `linear` or `scaled_linear`.
-        trained_betas (`np.ndarray`, optional):
-            option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
-        prediction_type (`str`, default `epsilon`, optional):
-            prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion
-            process), `sample` (directly predicting the noisy sample`) or `v_prediction` (see section 2.4
-            https://imagen.research.google/video/paper.pdf).
-        clip_sample (`bool`, default `True`):
-            option to clip predicted sample for numerical stability.
-        clip_sample_range (`float`, default `1.0`):
-            the maximum magnitude for sample clipping. Valid only when `clip_sample=True`.
+        trained_betas (`np.ndarray`, *optional*):
+            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
+        prediction_type (`str`, defaults to `epsilon`, *optional*):
+            Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
+            `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen
+            Video](https://imagen.research.google/video/paper.pdf) paper).
+        clip_sample (`bool`, defaults to `True`):
+            Clip the predicted sample for numerical stability.
+        clip_sample_range (`float`, defaults to 1.0):
+            The maximum magnitude for sample clipping. Valid only when `clip_sample=True`.
         use_karras_sigmas (`bool`, *optional*, defaults to `False`):
-             This parameter controls whether to use Karras sigmas (Karras et al. (2022) scheme) for step sizes in the
-             noise schedule during the sampling process. If True, the sigmas will be determined according to a sequence
-             of noise levels {σi} as defined in Equation (5) of the paper https://arxiv.org/pdf/2206.00364.pdf.
-        timestep_spacing (`str`, default `"linspace"`):
-            The way the timesteps should be scaled. Refer to Table 2. of [Common Diffusion Noise Schedules and Sample
-            Steps are Flawed](https://arxiv.org/abs/2305.08891) for more information.
-        steps_offset (`int`, default `0`):
-            an offset added to the inference steps. You can use a combination of `offset=1` and
-            `set_alpha_to_one=False`, to make the last step use step 0 for the previous alpha product, as done in
-            stable diffusion.
+            Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. If `True`,
+            the sigmas are determined according to a sequence of noise levels {σi}.
+        timestep_spacing (`str`, defaults to `"linspace"`):
+            The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
+            Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
+        steps_offset (`int`, defaults to 0):
+            An offset added to the inference steps. You can use a combination of `offset=1` and
+            `set_alpha_to_one=False` to make the last step use step 0 for the previous alpha product like in Stable
+            Diffusion.
     """
 
     _compatibles = [e.name for e in KarrasDiffusionSchedulers]
@@ -181,12 +181,18 @@ class HeunDiscreteScheduler(SchedulerMixin, ConfigMixin):
         timestep: Union[float, torch.FloatTensor],
     ) -> torch.FloatTensor:
         """
-        Args:
         Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
         current timestep.
-            sample (`torch.FloatTensor`): input sample timestep (`int`, optional): current timestep
+
+        Args:
+            sample (`torch.FloatTensor`):
+                The input sample.
+            timestep (`int`, *optional*):
+                The current timestep in the diffusion chain.
+
         Returns:
-            `torch.FloatTensor`: scaled input sample
+            `torch.FloatTensor`:
+                A scaled input sample.
         """
         step_index = self.index_for_timestep(timestep)
 
@@ -201,13 +207,13 @@ class HeunDiscreteScheduler(SchedulerMixin, ConfigMixin):
         num_train_timesteps: Optional[int] = None,
     ):
         """
-        Sets the timesteps used for the diffusion chain. Supporting function to be run before inference.
+        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
 
         Args:
             num_inference_steps (`int`):
-                the number of diffusion steps used when generating samples with a pre-trained model.
-            device (`str` or `torch.device`, optional):
-                the device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
+                The number of diffusion steps used when generating samples with a pre-trained model.
+            device (`str` or `torch.device`, *optional*):
+                The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
         """
         self.num_inference_steps = num_inference_steps
 
@@ -312,17 +318,23 @@ class HeunDiscreteScheduler(SchedulerMixin, ConfigMixin):
         return_dict: bool = True,
     ) -> Union[SchedulerOutput, Tuple]:
         """
-        Args:
-        Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
+        Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
         process from the learned model outputs (most often the predicted noise).
-            model_output (`torch.FloatTensor` or `np.ndarray`): direct output from learned diffusion model. timestep
-            (`int`): current discrete timestep in the diffusion chain. sample (`torch.FloatTensor` or `np.ndarray`):
-                current instance of sample being created by diffusion process.
-            return_dict (`bool`): option for returning tuple rather than SchedulerOutput class
+
+        Args:
+            model_output (`torch.FloatTensor`):
+                The direct output from learned diffusion model.
+            timestep (`float`):
+                The current discrete timestep in the diffusion chain.
+            sample (`torch.FloatTensor`):
+                A current instance of a sample created by the diffusion process.
+            return_dict (`bool`):
+                Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or tuple.
+
         Returns:
             [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
-            [`~schedulers.scheduling_utils.SchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When
-            returning a tuple, the first element is the sample tensor.
+                If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a
+                tuple is returned where the first element is the sample tensor.
         """
         step_index = self.index_for_timestep(timestep)
 

src/diffusers/schedulers/scheduling_ipndm.py

@@ -24,18 +24,16 @@ from .scheduling_utils import SchedulerMixin, SchedulerOutput
 
 class IPNDMScheduler(SchedulerMixin, ConfigMixin):
     """
-    Improved Pseudo numerical methods for diffusion models (iPNDM) ported from @crowsonkb's amazing k-diffusion
-    [library](https://github.com/crowsonkb/v-diffusion-pytorch/blob/987f8985e38208345c1959b0ea767a625831cc9b/diffusion/sampling.py#L296)
+    A fourth-order Improved Pseudo Linear Multistep scheduler.
 
-    [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
-    function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`.
-    [`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and
-    [`~SchedulerMixin.from_pretrained`] functions.
-
-    For more details, see the original paper: https://arxiv.org/abs/2202.09778
+    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
+    methods the library implements for all schedulers such as loading and saving.
 
     Args:
-        num_train_timesteps (`int`): number of diffusion steps used to train the model.
+        num_train_timesteps (`int`, defaults to 1000):
+            The number of diffusion steps to train the model.
+        trained_betas (`np.ndarray`, *optional*):
+            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
     """
 
     order = 1
@@ -60,11 +58,13 @@ class IPNDMScheduler(SchedulerMixin, ConfigMixin):
 
     def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
         """
-        Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.
+        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
 
         Args:
             num_inference_steps (`int`):
-                the number of diffusion steps used when generating samples with a pre-trained model.
+                The number of diffusion steps used when generating samples with a pre-trained model.
+            device (`str` or `torch.device`, *optional*):
+                The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
         """
         self.num_inference_steps = num_inference_steps
         steps = torch.linspace(1, 0, num_inference_steps + 1)[:-1]
@@ -90,20 +90,23 @@ class IPNDMScheduler(SchedulerMixin, ConfigMixin):
         return_dict: bool = True,
     ) -> Union[SchedulerOutput, Tuple]:
         """
-        Step function propagating the sample with the linear multi-step method. This has one forward pass with multiple
-        times to approximate the solution.
+        Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
+        the linear multistep method. It performs one forward pass multiple times to approximate the solution.
 
         Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`int`): current discrete timestep in the diffusion chain.
+            model_output (`torch.FloatTensor`):
+                The direct output from learned diffusion model.
+            timestep (`int`):
+                The current discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
-            return_dict (`bool`): option for returning tuple rather than SchedulerOutput class
+                A current instance of a sample created by the diffusion process.
+            return_dict (`bool`):
+                Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or tuple.
 
         Returns:
-            [`~scheduling_utils.SchedulerOutput`] or `tuple`: [`~scheduling_utils.SchedulerOutput`] if `return_dict` is
-            True, otherwise a `tuple`. When returning a tuple, the first element is the sample tensor.
-
+            [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
+                If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a
+                tuple is returned where the first element is the sample tensor.
         """
         if self.num_inference_steps is None:
             raise ValueError(
@@ -138,10 +141,12 @@ class IPNDMScheduler(SchedulerMixin, ConfigMixin):
         current timestep.
 
         Args:
-            sample (`torch.FloatTensor`): input sample
+            sample (`torch.FloatTensor`):
+                The input sample.
 
         Returns:
-            `torch.FloatTensor`: scaled input sample
+            `torch.FloatTensor`:
+                A scaled input sample.
         """
         return sample