[docs sprint] schedulers docs, will update (#376)

* init schedulers docs

* add some docstrings, fix sidebar formatting

* add docstrings

* [Type hint] PNDM schedulers (#335)

* [Type hint] PNDM Schedulers

* ran make style

* updated timesteps type hint

* apply suggestions from code review

* ran make style

* removed unused import

* [Type hint] scheduling ddim (#343)

* [Type hint] scheduling ddim

* apply suggestions from code review

apply suggestions to also return the return type
Co-authored-by: Patrick von Platen <patrick.v.platen@gmail.com>
Co-authored-by: Patrick von Platen <patrick.v.platen@gmail.com>

* make style

* update class docstrings

* add docstrings

* missed merge edit

* add general docs page

* modify headings for right sidebar
Co-authored-by: Partho <parthodas6176@gmail.com>
Co-authored-by: Santiago Víquez <santi.viquez@gmail.com>
Co-authored-by: Patrick von Platen <patrick.v.platen@gmail.com>

docs/source/api/schedulers.mdx

@@ -10,19 +10,95 @@ an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express o
 specific language governing permissions and limitations under the License.
 -->
 
-# Models
+# Schedulers
+
+Diffusers contains multiple pre-built schedule functions for the diffusion process.
+
+## What is a schduler?
+The schedule functions, denoted *Schedulers* in the library take in the output of a trained model, a sample which the diffusion process is iterating on, and a timestep to return a denoised sample.
+
+- Schedulers define the methodology for iteratively adding noise to an image or for updating a sample based on model outputs.
+    - adding noise in different manners represent the algorithmic processes to train a diffusion model by adding noise to images.
+    - for inference, the scheduler defines how to update a sample based on an output from a pretrained model.
+- Schedulers are often defined by a *noise schedule* and an *update rule* to solve the differential equation solution.
+
+### Discrete versus continuous schedulers
+All schedulers take in a timestep to predict the updated version of the sample being diffused.
+The timesteps dictate where in the diffusion process the step is, where data is generated by iterating forward in time and inference is executed by propagating backwards through timesteps.
+Different algorithms use timesteps that both discrete (accepting `int` inputs), such as the [`DDPMScheduler`] or [`PNDMScheduler`], and continuous (accepting 'float` inputs), such as the score-based schedulers [`ScoreSdeVeScheduler`] or [`ScoreSdeVpScheduler`].
+
+## Designing Re-usable schedulers
+The core design principle between the schedule functions is to be model, system, and framework independent.
+This allows for rapid experimentation and cleaner abstractions in the code, where the model prediction is separated from the sample update.
+To this end, the design of schedulers is such that:
+- Schedulers can be used interchangeably between diffusion models in inference to find the preferred trade-off between speed and generation quality.
+- Schedulers are currently by default in PyTorch, but are designed to be framework independent (partial Numpy support currently exists).
 
-Diffusers contains pretrained models for popular algorithms and modules for creating the next set of diffusion models.
-The primary function of these models is to denoise an input sample, by modeling the distribution $p_\theta(\mathbf{x}_{t-1}|\mathbf{x}_t)$.
-The models are built on the base class ['ModelMixin'] that is a `torch.nn.module` with basic functionality for saving and loading models both locally and from the HuggingFace hub.
 
 ## API
+The core API for any new scheduler must follow a limited structure.
+- Schedulers should provide one or more `def step(...)` functions that should be called to update the generated sample iteratively.
+- Schedulers should provide a `set_timesteps(...)` method that configures the parameters of a schedule function for a specific inference task.
+- Schedulers should be framework-agonstic, but provide a simple functionality to convert the scheduler into a specific framework, such as PyTorch
+with a `set_format(...)` method.
+
+### Core
+The base class [`SchedulerMixin`] implements low level utilities used by multiple schedulers.
+
+#### SchedulerMixin
+[[autodoc]] SchedulerMixin
+
+#### SchedulerOutput
+The class [`SchedulerOutput`] contains the ouputs from any schedulers `step(...)` call.
+[[autodoc]] schedulers.scheduling_utils.SchedulerOutput
+
+### Existing Schedulers
+
+#### Denoising diffusion implicit models (DDIM)
+
+Original paper can be found here.
+
+[[autodoc]] schedulers.scheduling_ddim.DDIMScheduler
+
+#### Denoising diffusion probabilistic models (DDPM)
+
+Original paper can be found [here](https://arxiv.org/abs/2010.02502).
+
+[[autodoc]] schedulers.scheduling_ddpm.DDPMScheduler
+
+#### Varience exploding, stochastic sampling from Karras et. al
+
+Original paper can be found [here](https://arxiv.org/abs/2006.11239).
+
+[[autodoc]] schedulers.scheduling_karras_ve.KarrasVeScheduler
+
+#### Linear multistep scheduler for discrete beta schedules
+
+Original implementation can be found [here](https://arxiv.org/abs/2206.00364).
+
+
+[[autodoc]] schedulers.scheduling_lms_discrete.LMSDiscreteScheduler
+
+#### Pseudo numerical methods for diffusion models (PNDM)
+
+Original implementation can be found [here](https://github.com/crowsonkb/k-diffusion/blob/481677d114f6ea445aa009cf5bd7a9cdee909e47/k_diffusion/sampling.py#L181).
+
+[[autodoc]] schedulers.scheduling_pndm.PNDMScheduler
+
+#### variance exploding stochastic differential equation (SDE) scheduler
+
+Original paper can be found [here](https://arxiv.org/abs/2011.13456).
+
+[[autodoc]] schedulers.scheduling_sde_ve.ScoreSdeVeScheduler
+
+#### variance preserving stochastic differential equation (SDE) scheduler
+
+Original paper can be found [here](https://arxiv.org/abs/2011.13456).
+
+<Tip warning={true}>
 
-Models should provide the `def forward` function and initialization of the model.
-All saving, loading, and utilities should be in the base ['ModelMixin'] class.
+Score SDE-VP is under construction.
 
-## Examples
+</Tip>
 
-- The ['UNetModel'] was proposed in [TODO](https://arxiv.org/) and has been used in paper1, paper2, paper3.
-- Extensions of the ['UNetModel'] include the ['UNetGlideModel'] that uses attention and timestep embeddings for the [GLIDE](https://arxiv.org/abs/2112.10741) paper, the ['UNetGradTTS'] model from this [paper](https://arxiv.org/abs/2105.06337) for text-to-speech, ['UNetLDMModel'] for latent-diffusion models in this [paper](https://arxiv.org/abs/2112.10752), and the ['TemporalUNet'] used for time-series prediciton in this reinforcement learning [paper](https://arxiv.org/abs/2205.09991).
-- TODO: mention VAE / SDE score estimation
+[[autodoc]] schedulers.scheduling_sde_vp.ScoreSdeVpScheduler
\ No newline at end of file

src/diffusers/schedulers/scheduling_ddim.py

@@ -30,11 +30,17 @@ def betas_for_alpha_bar(num_diffusion_timesteps, max_beta=0.999):
     Create a beta schedule that discretizes the given alpha_t_bar function, which defines the cumulative product of
     (1-beta) over time from t = [0,1].
 
-    :param num_diffusion_timesteps: the number of betas to produce. :param alpha_bar: a lambda that takes an argument t
-    from 0 to 1 and
-                      produces the cumulative product of (1-beta) up to that part of the diffusion process.
-    :param max_beta: the maximum beta to use; use values lower than 1 to
+    Contains a function alpha_bar that takes an argument t and transforms it to the cumulative product of (1-beta) up
+    to that part of the diffusion process.
+
+
+    Args:
+        num_diffusion_timesteps (`int`): the number of betas to produce.
+        max_beta (`float`): the maximum beta to use; use values lower than 1 to
                      prevent singularities.
+
+    Returns:
+        betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
     """
 
     def alpha_bar(time_step):
@@ -49,6 +55,29 @@ def betas_for_alpha_bar(num_diffusion_timesteps, max_beta=0.999):
 
 
 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.
+
+    For more details, see the original paper: https://arxiv.org/abs/2010.02502
+
+    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`, or `squaredcos_cap_v2`.
+        trained_betas (`np.ndarray`, optional): TODO
+        timestep_values (`np.ndarray`, optional): TODO
+        clip_sample (`bool`, default `True`):
+            option to clip predicted sample between -1 and 1 for numerical stability.
+        set_alpha_to_one (`bool`, default `True`):
+            if alpha for final step is 1 or the final alpha of the "non-previous" one.
+        tensor_format (`str`): whether the scheduler expects pytorch or numpy arrays.
+
+    """
+
     @register_to_config
     def __init__(
         self,
@@ -62,7 +91,8 @@ class DDIMScheduler(SchedulerMixin, ConfigMixin):
         set_alpha_to_one: bool = True,
         tensor_format: str = "pt",
     ):
-
+        if trained_betas is not None:
+            self.betas = np.asarray(trained_betas)
         if beta_schedule == "linear":
             self.betas = np.linspace(beta_start, beta_end, num_train_timesteps, dtype=np.float32)
         elif beta_schedule == "scaled_linear":
@@ -101,6 +131,14 @@ class DDIMScheduler(SchedulerMixin, ConfigMixin):
         return variance
 
     def set_timesteps(self, num_inference_steps: int, offset: int = 0):
+        """
+        Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.
+
+        Args:
+            num_inference_steps (`int`):
+                the number of diffusion steps used when generating samples with a pre-trained model.
+            offset (`int`): TODO
+        """
         self.num_inference_steps = num_inference_steps
         self.timesteps = np.arange(
             0, self.config.num_train_timesteps, self.config.num_train_timesteps // self.num_inference_steps
@@ -118,7 +156,24 @@ class DDIMScheduler(SchedulerMixin, ConfigMixin):
         generator=None,
         return_dict: bool = True,
     ) -> Union[SchedulerOutput, Tuple]:
-
+        """
+        Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
+        process from the learned model outputs (most often the predicted noise).
+
+        Args:
+            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.
+            eta (`float`): weight of noise for added noise in diffusion step.
+            use_clipped_model_output (`bool`): TODO
+            generator: random number generator.
+            return_dict (`bool`): option for returning tuple rather than SchedulerOutput class
+
+        Returns:
+            `SchedulerOutput`: updated sample in the diffusion chain.
+
+        """
         if self.num_inference_steps is None:
             raise ValueError(
                 "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"

src/diffusers/schedulers/scheduling_ddpm.py

@@ -29,11 +29,17 @@ def betas_for_alpha_bar(num_diffusion_timesteps, max_beta=0.999):
     Create a beta schedule that discretizes the given alpha_t_bar function, which defines the cumulative product of
     (1-beta) over time from t = [0,1].
 
-    :param num_diffusion_timesteps: the number of betas to produce. :param alpha_bar: a lambda that takes an argument t
-    from 0 to 1 and
-                      produces the cumulative product of (1-beta) up to that part of the diffusion process.
-    :param max_beta: the maximum beta to use; use values lower than 1 to
+    Contains a function alpha_bar that takes an argument t and transforms it to the cumulative product of (1-beta) up
+    to that part of the diffusion process.
+
+
+    Args:
+        num_diffusion_timesteps (`int`): the number of betas to produce.
+        max_beta (`float`): the maximum beta to use; use values lower than 1 to
                      prevent singularities.
+
+    Returns:
+        betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
     """
 
     def alpha_bar(time_step):
@@ -48,6 +54,29 @@ def betas_for_alpha_bar(num_diffusion_timesteps, max_beta=0.999):
 
 
 class DDPMScheduler(SchedulerMixin, ConfigMixin):
+    """
+    Denoising diffusion probabilistic models (DDPMs) explores the connections between denoising score matching and
+    Langevin dynamics sampling.
+
+    For more details, see the original paper: https://arxiv.org/abs/2006.11239
+
+    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`, or `squaredcos_cap_v2`.
+        trained_betas (`np.ndarray`, optional): TODO
+        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 between -1 and 1 for numerical stability.
+        tensor_format (`str`): whether the scheduler expects pytorch or numpy arrays.
+
+    """
+
     @register_to_config
     def __init__(
         self,
@@ -88,6 +117,13 @@ class DDPMScheduler(SchedulerMixin, ConfigMixin):
         self.variance_type = variance_type
 
     def set_timesteps(self, num_inference_steps: int):
+        """
+        Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.
+
+        Args:
+            num_inference_steps (`int`):
+                the number of diffusion steps used when generating samples with a pre-trained model.
+        """
         num_inference_steps = min(self.config.num_train_timesteps, num_inference_steps)
         self.num_inference_steps = num_inference_steps
         self.timesteps = np.arange(
@@ -137,7 +173,25 @@ class DDPMScheduler(SchedulerMixin, ConfigMixin):
         generator=None,
         return_dict: bool = True,
     ) -> Union[SchedulerOutput, Tuple]:
-
+        """
+        Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
+        process from the learned model outputs (most often the predicted noise).
+
+        Args:
+            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.
+            eta (`float`): weight of noise for added noise in diffusion step.
+            predict_epsilon (`bool`):
+                optional flag to use when model predicts the samples directly instead of the noise, epsilon.
+            generator: random number generator.
+            return_dict (`bool`): option for returning tuple rather than SchedulerOutput class
+
+        Returns:
+            `SchedulerOutput`: updated sample in the diffusion chain.
+
+        """
         t = timestep
 
         if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type in ["learned", "learned_range"]:

src/diffusers/schedulers/scheduling_karras_ve.py

@@ -49,6 +49,24 @@ class KarrasVeScheduler(SchedulerMixin, ConfigMixin):
     [1] Karras, Tero, et al. "Elucidating the Design Space of Diffusion-Based Generative Models."
     https://arxiv.org/abs/2206.00364 [2] Song, Yang, et al. "Score-based generative modeling through stochastic
     differential equations." https://arxiv.org/abs/2011.13456
+
+    For more details on the parameters, see the original paper's Appendix E.: "Elucidating the Design Space of
+    Diffusion-Based Generative Models." https://arxiv.org/abs/2206.00364. The grid search values used to find the
+    optimal {s_noise, s_churn, s_min, s_max} for a specific model are described in Table 5 of the paper.
+
+    Args:
+        sigma_min (`float`): minimum noise magnitude
+        sigma_max (`float`): maximum noise magnitude
+        s_noise (`float`): the amount of additional noise to counteract loss of detail during sampling.
+            A reasonable range is [1.000, 1.011].
+        s_churn (`float`): the parameter controlling the overall amount of stochasticity.
+            A reasonable range is [0, 100].
+        s_min (`float`): the start value of the sigma range where we add noise (enable stochasticity).
+            A reasonable range is [0, 10].
+        s_max (`float`): the end value of the sigma range where we add noise.
+            A reasonable range is [0.2, 80].
+        tensor_format (`str`): whether the scheduler expects pytorch or numpy arrays.
+
     """
 
     @register_to_config
@@ -62,23 +80,6 @@ class KarrasVeScheduler(SchedulerMixin, ConfigMixin):
         s_max: float = 50,
         tensor_format: str = "pt",
     ):
-        """
-        For more details on the parameters, see the original paper's Appendix E.: "Elucidating the Design Space of
-        Diffusion-Based Generative Models." https://arxiv.org/abs/2206.00364. The grid search values used to find the
-        optimal {s_noise, s_churn, s_min, s_max} for a specific model are described in Table 5 of the paper.
-
-        Args:
-            sigma_min (`float`): minimum noise magnitude
-            sigma_max (`float`): maximum noise magnitude
-            s_noise (`float`): the amount of additional noise to counteract loss of detail during sampling.
-                A reasonable range is [1.000, 1.011].
-            s_churn (`float`): the parameter controlling the overall amount of stochasticity.
-                A reasonable range is [0, 100].
-            s_min (`float`): the start value of the sigma range where we add noise (enable stochasticity).
-                A reasonable range is [0, 10].
-            s_max (`float`): the end value of the sigma range where we add noise.
-                A reasonable range is [0.2, 80].
-        """
         # setable values
         self.num_inference_steps = None
         self.timesteps = None
@@ -88,6 +89,14 @@ class KarrasVeScheduler(SchedulerMixin, ConfigMixin):
         self.set_format(tensor_format=tensor_format)
 
     def set_timesteps(self, num_inference_steps: int):
+        """
+        Sets the continuous timesteps used for the diffusion chain. Supporting function to be run before inference.
+
+        Args:
+            num_inference_steps (`int`):
+                the number of diffusion steps used when generating samples with a pre-trained model.
+
+        """
         self.num_inference_steps = num_inference_steps
         self.timesteps = np.arange(0, self.num_inference_steps)[::-1].copy()
         self.schedule = [
@@ -104,6 +113,8 @@ class KarrasVeScheduler(SchedulerMixin, ConfigMixin):
         """
         Explicit Langevin-like "churn" step of adding noise to the sample according to a factor gamma_i ≥ 0 to reach a
         higher noise level sigma_hat = sigma_i + gamma_i*sigma_i.
+
+        TODO Args:
         """
         if self.s_min <= sigma <= self.s_max:
             gamma = min(self.s_churn / self.num_inference_steps, 2**0.5 - 1)
@@ -125,6 +136,21 @@ class KarrasVeScheduler(SchedulerMixin, ConfigMixin):
         sample_hat: Union[torch.FloatTensor, np.ndarray],
         return_dict: bool = True,
     ) -> Union[KarrasVeOutput, Tuple]:
+        """
+        Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
+        process from the learned model outputs (most often the predicted noise).
+
+        Args:
+            model_output (`torch.FloatTensor` or `np.ndarray`): direct output from learned diffusion model.
+            sigma_hat (`float`): TODO
+            sigma_prev (`float`): TODO
+            sample_hat (`torch.FloatTensor` or `np.ndarray`): TODO
+            return_dict (`bool`): option for returning tuple rather than SchedulerOutput class
+
+        Returns:
+            KarrasVeOutput: updated sample in the diffusion chain and derivative (TODO double check).
+
+        """
 
         pred_original_sample = sample_hat + sigma_hat * model_output
         derivative = (sample_hat - pred_original_sample) / sigma_hat
@@ -145,7 +171,22 @@ class KarrasVeScheduler(SchedulerMixin, ConfigMixin):
         derivative: Union[torch.FloatTensor, np.ndarray],
         return_dict: bool = True,
     ) -> Union[KarrasVeOutput, Tuple]:
+        """
+        Correct the predicted sample based on the output model_output of the network. TODO complete description
+
+        Args:
+            model_output (`torch.FloatTensor` or `np.ndarray`): direct output from learned diffusion model.
+            sigma_hat (`float`): TODO
+            sigma_prev (`float`): TODO
+            sample_hat (`torch.FloatTensor` or `np.ndarray`): TODO
+            sample_prev (`torch.FloatTensor` or `np.ndarray`): TODO
+            derivative (`torch.FloatTensor` or `np.ndarray`): TODO
+            return_dict (`bool`): option for returning tuple rather than SchedulerOutput class
+
+        Returns:
+            prev_sample (TODO): updated sample in the diffusion chain. derivative (TODO): TODO
 
+        """
         pred_original_sample = sample_prev + sigma_prev * model_output
         derivative_corr = (sample_prev - pred_original_sample) / sigma_prev
         sample_prev = sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

src/diffusers/schedulers/scheduling_lms_discrete.py

@@ -24,6 +24,26 @@ from .scheduling_utils import SchedulerMixin, SchedulerOutput
 
 
 class LMSDiscreteScheduler(SchedulerMixin, ConfigMixin):
+    """
+    Linear Multistep Scheduler 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#L181
+
+    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` or `scaled_linear`.
+        trained_betas (`np.ndarray`, optional): TODO
+            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`.
+        timestep_values (`np.ndarry`, optional): TODO
+        tensor_format (`str`): whether the scheduler expects pytorch or numpy arrays.
+
+    """
+
     @register_to_config
     def __init__(
         self,
@@ -35,12 +55,8 @@ class LMSDiscreteScheduler(SchedulerMixin, ConfigMixin):
         timestep_values: Optional[np.ndarray] = None,
         tensor_format: str = "pt",
     ):
-        """
-        Linear Multistep Scheduler 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#L181
-        """
-
+        if trained_betas is not None:
+            self.betas = np.asarray(trained_betas)
         if beta_schedule == "linear":
             self.betas = np.linspace(beta_start, beta_end, num_train_timesteps, dtype=np.float32)
         elif beta_schedule == "scaled_linear":
@@ -64,7 +80,12 @@ class LMSDiscreteScheduler(SchedulerMixin, ConfigMixin):
 
     def get_lms_coefficient(self, order, t, current_order):
         """
-        Compute a linear multistep coefficient
+        Compute a linear multistep coefficient.
+
+        Args:
+            order (TODO):
+            t (TODO):
+            current_order (TODO):
         """
 
         def lms_derivative(tau):
@@ -80,6 +101,13 @@ class LMSDiscreteScheduler(SchedulerMixin, ConfigMixin):
         return integrated_coeff
 
     def set_timesteps(self, num_inference_steps: int):
+        """
+        Sets the timesteps used for the diffusion chain. Supporting function to be run before inference.
+
+        Args:
+            num_inference_steps (`int`):
+                the number of diffusion steps used when generating samples with a pre-trained model.
+        """
         self.num_inference_steps = num_inference_steps
         self.timesteps = np.linspace(self.num_train_timesteps - 1, 0, num_inference_steps, dtype=float)
 
@@ -102,6 +130,22 @@ class LMSDiscreteScheduler(SchedulerMixin, ConfigMixin):
         order: int = 4,
         return_dict: bool = True,
     ) -> Union[SchedulerOutput, Tuple]:
+        """
+        Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
+        process from the learned model outputs (most often the predicted noise).
+
+        Args:
+            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.
+            order: coefficient for multi-step inference.
+            return_dict (`bool`): option for returning tuple rather than SchedulerOutput class
+
+        Returns:
+            prev_sample (`SchedulerOutput` or `Tuple`): updated sample in the diffusion chain.
+
+        """
         sigma = self.sigmas[timestep]
 
         # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise

src/diffusers/schedulers/scheduling_pndm.py

@@ -15,7 +15,7 @@
 # DISCLAIMER: This file is strongly influenced by https://github.com/ermongroup/ddim
 
 import math
-from typing import Tuple, Union
+from typing import Optional, Tuple, Union
 
 import numpy as np
 import torch
@@ -29,11 +29,17 @@ def betas_for_alpha_bar(num_diffusion_timesteps, max_beta=0.999):
     Create a beta schedule that discretizes the given alpha_t_bar function, which defines the cumulative product of
     (1-beta) over time from t = [0,1].
 
-    :param num_diffusion_timesteps: the number of betas to produce. :param alpha_bar: a lambda that takes an argument t
-    from 0 to 1 and
-                      produces the cumulative product of (1-beta) up to that part of the diffusion process.
-    :param max_beta: the maximum beta to use; use values lower than 1 to
+    Contains a function alpha_bar that takes an argument t and transforms it to the cumulative product of (1-beta) up
+    to that part of the diffusion process.
+
+
+    Args:
+        num_diffusion_timesteps (`int`): the number of betas to produce.
+        max_beta (`float`): the maximum beta to use; use values lower than 1 to
                      prevent singularities.
+
+    Returns:
+        betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
     """
 
     def alpha_bar(time_step):
@@ -48,6 +54,27 @@ def betas_for_alpha_bar(num_diffusion_timesteps, max_beta=0.999):
 
 
 class PNDMScheduler(SchedulerMixin, ConfigMixin):
+    """
+    Pseudo numerical methods for diffusion models (PNDM) proposes using more advanced ODE integration techniques,
+    namely Runge-Kutta method and a linear multi-step method.
+
+    For more details, see the original paper: https://arxiv.org/abs/2202.09778
+
+    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`, or `squaredcos_cap_v2`.
+        trained_betas (`np.ndarray`, optional): TODO
+        tensor_format (`str`): whether the scheduler expects pytorch or numpy arrays
+        skip_prk_steps (`bool`):
+            allows the scheduler to skip the Runge-Kutta steps that are defined in the original paper as being required
+            before plms steps; defaults to `False`.
+
+    """
+
     @register_to_config
     def __init__(
         self,
@@ -55,10 +82,12 @@ class PNDMScheduler(SchedulerMixin, ConfigMixin):
         beta_start: float = 0.0001,
         beta_end: float = 0.02,
         beta_schedule: str = "linear",
+        trained_betas: Optional[np.ndarray] = None,
         tensor_format: str = "pt",
         skip_prk_steps: bool = False,
     ):
-
+        if trained_betas is not None:
+            self.betas = np.asarray(trained_betas)
         if beta_schedule == "linear":
             self.betas = np.linspace(beta_start, beta_end, num_train_timesteps, dtype=np.float32)
         elif beta_schedule == "scaled_linear":
@@ -98,6 +127,14 @@ class PNDMScheduler(SchedulerMixin, ConfigMixin):
         self.set_format(tensor_format=tensor_format)
 
     def set_timesteps(self, num_inference_steps: int, offset: int = 0) -> torch.FloatTensor:
+        """
+        Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.
+
+        Args:
+            num_inference_steps (`int`):
+                the number of diffusion steps used when generating samples with a pre-trained model.
+            offset (`int`): TODO
+        """
         self.num_inference_steps = num_inference_steps
         self._timesteps = list(
             range(0, self.config.num_train_timesteps, self.config.num_train_timesteps // num_inference_steps)
@@ -135,7 +172,23 @@ class PNDMScheduler(SchedulerMixin, ConfigMixin):
         sample: Union[torch.FloatTensor, np.ndarray],
         return_dict: bool = True,
     ) -> Union[SchedulerOutput, Tuple]:
+        """
+        Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
+        process from the learned model outputs (most often the predicted noise).
+
+        This function calls `step_prk()` or `step_plms()` depending on the internal variable `counter`.
+
+        Args:
+            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
 
+        Returns:
+            `SchedulerOutput`: updated sample in the diffusion chain.
+
+        """
         if self.counter < len(self.prk_timesteps) and not self.config.skip_prk_steps:
             return self.step_prk(model_output=model_output, timestep=timestep, sample=sample, return_dict=return_dict)
         else:
@@ -151,6 +204,17 @@ class PNDMScheduler(SchedulerMixin, ConfigMixin):
         """
         Step function propagating the sample with the Runge-Kutta method. RK takes 4 forward passes to approximate the
         solution to the differential equation.
+
+        Args:
+            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
+
+        Returns:
+            prev_sample (`SchedulerOutput` or `Tuple`): updated sample in the diffusion chain.
+
         """
         if self.num_inference_steps is None:
             raise ValueError(
@@ -194,6 +258,17 @@ class PNDMScheduler(SchedulerMixin, ConfigMixin):
         """
         Step function propagating the sample with the linear multi-step method. This has one forward pass with multiple
         times to approximate the solution.
+
+        Args:
+            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
+
+        Returns:
+            prev_sample (`SchedulerOutput` or `Tuple`): updated sample in the diffusion chain.
+
         """
         if self.num_inference_steps is None:
             raise ValueError(

src/diffusers/schedulers/scheduling_sde_ve.py

@@ -47,12 +47,19 @@ class ScoreSdeVeScheduler(SchedulerMixin, ConfigMixin):
     """
     The variance exploding stochastic differential equation (SDE) scheduler.
 
-    :param snr: coefficient weighting the step from the model_output sample (from the network) to the random noise.
-    :param sigma_min: initial noise scale for sigma sequence in sampling procedure. The minimum sigma should mirror the
-            distribution of the data.
-    :param sigma_max: :param sampling_eps: the end value of sampling, where timesteps decrease progessively from 1 to
-    epsilon. :param correct_steps: number of correction steps performed on a produced sample. :param tensor_format:
-    "np" or "pt" for the expected format of samples passed to the Scheduler.
+    For more information, see the original paper: https://arxiv.org/abs/2011.13456
+
+    Args:
+        snr (`float`):
+            coefficient weighting the step from the model_output sample (from the network) to the random noise.
+        sigma_min (`float`):
+                initial noise scale for sigma sequence in sampling procedure. The minimum sigma should mirror the
+                distribution of the data.
+        sigma_max (`float`): maximum value used for the range of continuous timesteps passed into the model.
+        sampling_eps (`float`): the end value of sampling, where timesteps decrease progessively from 1 to
+        epsilon.
+        correct_steps (`int`): number of correction steps performed on a produced sample.
+        tensor_format (`str`): "np" or "pt" for the expected format of samples passed to the Scheduler.
     """
 
     @register_to_config
@@ -66,11 +73,7 @@ class ScoreSdeVeScheduler(SchedulerMixin, ConfigMixin):
         correct_steps=1,
         tensor_format="pt",
     ):
-        # self.sigmas = None
-        # self.discrete_sigmas = None
-        #
-        # # setable values
-        # self.num_inference_steps = None
+        # setable values
         self.timesteps = None
 
         self.set_sigmas(num_train_timesteps, sigma_min, sigma_max, sampling_eps)
@@ -79,6 +82,15 @@ class ScoreSdeVeScheduler(SchedulerMixin, ConfigMixin):
         self.set_format(tensor_format=tensor_format)
 
     def set_timesteps(self, num_inference_steps, sampling_eps=None):
+        """
+        Sets the continuous timesteps used for the diffusion chain. Supporting function to be run before inference.
+
+        Args:
+            num_inference_steps (`int`):
+                the number of diffusion steps used when generating samples with a pre-trained model.
+            sampling_eps (`float`, optional): final timestep value (overrides value given at Scheduler instantiation).
+
+        """
         sampling_eps = sampling_eps if sampling_eps is not None else self.config.sampling_eps
         tensor_format = getattr(self, "tensor_format", "pt")
         if tensor_format == "np":
@@ -89,6 +101,20 @@ class ScoreSdeVeScheduler(SchedulerMixin, ConfigMixin):
             raise ValueError(f"`self.tensor_format`: {self.tensor_format} is not valid.")
 
     def set_sigmas(self, num_inference_steps, sigma_min=None, sigma_max=None, sampling_eps=None):
+        """
+        Sets the noise scales used for the diffusion chain. Supporting function to be run before inference.
+
+        The sigmas control the weight of the `drift` and `diffusion` components of sample update.
+
+        Args:
+            num_inference_steps (`int`):
+                the number of diffusion steps used when generating samples with a pre-trained model.
+            sigma_min (`float`, optional):
+                initial noise scale value (overrides value given at Scheduler instantiation).
+            sigma_max (`float`, optional): final noise scale value (overrides value given at Scheduler instantiation).
+            sampling_eps (`float`, optional): final timestep value (overrides value given at Scheduler instantiation).
+
+        """
         sigma_min = sigma_min if sigma_min is not None else self.config.sigma_min
         sigma_max = sigma_max if sigma_max is not None else self.config.sigma_max
         sampling_eps = sampling_eps if sampling_eps is not None else self.config.sampling_eps
@@ -140,7 +166,20 @@ class ScoreSdeVeScheduler(SchedulerMixin, ConfigMixin):
         **kwargs,
     ) -> Union[SdeVeOutput, Tuple]:
         """
-        Predict the sample at the previous timestep by reversing the SDE.
+        Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
+        process from the learned model outputs (most often the predicted noise).
+
+        Args:
+            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.
+            generator: random number generator.
+            return_dict (`bool`): option for returning tuple rather than SchedulerOutput class
+
+        Returns:
+            prev_sample (`SchedulerOutput` or `Tuple`): updated sample in the diffusion chain.
+
         """
         if "seed" in kwargs and kwargs["seed"] is not None:
             self.set_seed(kwargs["seed"])
@@ -186,6 +225,17 @@ class ScoreSdeVeScheduler(SchedulerMixin, ConfigMixin):
         """
         Correct the predicted sample based on the output model_output of the network. This is often run repeatedly
         after making the prediction for the previous timestep.
+
+        Args:
+            model_output (`torch.FloatTensor` or `np.ndarray`): direct output from learned diffusion model.
+            sample (`torch.FloatTensor` or `np.ndarray`):
+                current instance of sample being created by diffusion process.
+            generator: random number generator.
+            return_dict (`bool`): option for returning tuple rather than SchedulerOutput class
+
+        Returns:
+            prev_sample (`SchedulerOutput` or `Tuple`): updated sample in the diffusion chain.
+
         """
         if "seed" in kwargs and kwargs["seed"] is not None:
             self.set_seed(kwargs["seed"])

src/diffusers/schedulers/scheduling_sde_vp.py

@@ -24,6 +24,15 @@ from .scheduling_utils import SchedulerMixin
 
 
 class ScoreSdeVpScheduler(SchedulerMixin, ConfigMixin):
+    """
+    The variance preserving stochastic differential equation (SDE) scheduler.
+
+    For more information, see the original paper: https://arxiv.org/abs/2011.13456
+
+    UNDER CONSTRUCTION
+
+    """
+
     @register_to_config
     def __init__(self, num_train_timesteps=2000, beta_min=0.1, beta_max=20, sampling_eps=1e-3, tensor_format="np"):
 

src/diffusers/schedulers/scheduling_utils.py

@@ -38,6 +38,9 @@ class SchedulerOutput(BaseOutput):
 
 
 class SchedulerMixin:
+    """
+    Mixin containing common functions for the schedulers.
+    """
 
     config_name = SCHEDULER_CONFIG_NAME
     ignore_for_config = ["tensor_format"]