Add 2nd order heun scheduler (#1336)

* Add heun

* Finish first version of heun

* remove bogus

* finish

* finish

* improve

* up

* up

* fix more

* change progress bar

* Update src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion.py

* finish

* up

* up

* up

src/diffusers/__init__.py

@@ -46,6 +46,7 @@ if is_torch_available():
         DPMSolverMultistepScheduler,
         EulerAncestralDiscreteScheduler,
         EulerDiscreteScheduler,
+        HeunDiscreteScheduler,
         IPNDMScheduler,
         KarrasVeScheduler,
         PNDMScheduler,

src/diffusers/pipeline_utils.py

@@ -129,8 +129,8 @@ def is_safetensors_compatible(info) -> bool:
             sf_filename = os.path.join(prefix, "model.safetensors")
         else:
             sf_filename = pt_filename[: -len(".bin")] + ".safetensors"
-        if sf_filename not in filenames:
-            logger.warning("{sf_filename} not found")
+        if is_safetensors_compatible and sf_filename not in filenames:
+            logger.warning(f"{sf_filename} not found")
             is_safetensors_compatible = False
     return is_safetensors_compatible
 
@@ -767,7 +767,7 @@ class DiffusionPipeline(ConfigMixin):
 
         return pil_images
 
-    def progress_bar(self, iterable):
+    def progress_bar(self, iterable=None, total=None):
         if not hasattr(self, "_progress_bar_config"):
             self._progress_bar_config = {}
         elif not isinstance(self._progress_bar_config, dict):
@@ -775,7 +775,12 @@ class DiffusionPipeline(ConfigMixin):
                 f"`self._progress_bar_config` should be of type `dict`, but is {type(self._progress_bar_config)}."
             )
 
+        if iterable is not None:
             return tqdm(iterable, **self._progress_bar_config)
+        elif total is not None:
+            return tqdm(total=total, **self._progress_bar_config)
+        else:
+            raise ValueError("Either `total` or `iterable` has to be defined.")
 
     def set_progress_bar_config(self, **kwargs):
         self._progress_bar_config = kwargs

src/diffusers/pipelines/alt_diffusion/pipeline_alt_diffusion.py

@@ -541,7 +541,9 @@ class AltDiffusionPipeline(DiffusionPipeline):
         extra_step_kwargs = self.prepare_extra_step_kwargs(generator, eta)
 
         # 7. Denoising loop
-        for i, t in enumerate(self.progress_bar(timesteps)):
+        num_warmup_steps = len(timesteps) - num_inference_steps * self.scheduler.order
+        with self.progress_bar(total=num_inference_steps) as progress_bar:
+            for i, t in enumerate(timesteps):
                 # expand the latents if we are doing classifier free guidance
                 latent_model_input = torch.cat([latents] * 2) if do_classifier_free_guidance else latents
                 latent_model_input = self.scheduler.scale_model_input(latent_model_input, t)
@@ -558,6 +560,8 @@ class AltDiffusionPipeline(DiffusionPipeline):
                     latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample
 
                 # call the callback, if provided
+                if (i + 1) > num_warmup_steps and (i + 1) % self.scheduler.order == 0:
+                    progress_bar.update()
                     if callback is not None and i % callback_steps == 0:
                         callback(i, t, latents)
 

src/diffusers/pipelines/alt_diffusion/pipeline_alt_diffusion_img2img.py

@@ -433,7 +433,7 @@ class AltDiffusionImg2ImgPipeline(DiffusionPipeline):
         t_start = max(num_inference_steps - init_timestep + offset, 0)
         timesteps = self.scheduler.timesteps[t_start:]
 
-        return timesteps
+        return timesteps, num_inference_steps - t_start
 
     def prepare_latents(self, init_image, timestep, batch_size, num_images_per_prompt, dtype, device, generator=None):
         init_image = init_image.to(device=device, dtype=dtype)
@@ -562,7 +562,7 @@ class AltDiffusionImg2ImgPipeline(DiffusionPipeline):
 
         # 5. set timesteps
         self.scheduler.set_timesteps(num_inference_steps, device=device)
-        timesteps = self.get_timesteps(num_inference_steps, strength, device)
+        timesteps, num_inference_steps = self.get_timesteps(num_inference_steps, strength, device)
         latent_timestep = timesteps[:1].repeat(batch_size * num_images_per_prompt)
 
         # 6. Prepare latent variables
@@ -574,7 +574,9 @@ class AltDiffusionImg2ImgPipeline(DiffusionPipeline):
         extra_step_kwargs = self.prepare_extra_step_kwargs(generator, eta)
 
         # 8. Denoising loop
-        for i, t in enumerate(self.progress_bar(timesteps)):
+        num_warmup_steps = len(timesteps) - num_inference_steps * self.scheduler.order
+        with self.progress_bar(total=num_inference_steps) as progress_bar:
+            for i, t in enumerate(timesteps):
                 # expand the latents if we are doing classifier free guidance
                 latent_model_input = torch.cat([latents] * 2) if do_classifier_free_guidance else latents
                 latent_model_input = self.scheduler.scale_model_input(latent_model_input, t)
@@ -591,6 +593,8 @@ class AltDiffusionImg2ImgPipeline(DiffusionPipeline):
                 latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample
 
                 # call the callback, if provided
+                if (i + 1) > num_warmup_steps and (i + 1) % self.scheduler.order == 0:
+                    progress_bar.update()
                     if callback is not None and i % callback_steps == 0:
                         callback(i, t, latents)
 

src/diffusers/pipelines/stable_diffusion/pipeline_cycle_diffusion.py

@@ -475,7 +475,7 @@ class CycleDiffusionPipeline(DiffusionPipeline):
         t_start = max(num_inference_steps - init_timestep + offset, 0)
         timesteps = self.scheduler.timesteps[t_start:]
 
-        return timesteps
+        return timesteps, num_inference_steps - t_start
 
     def prepare_latents(self, init_image, timestep, batch_size, num_images_per_prompt, dtype, device, generator=None):
         init_image = init_image.to(device=device, dtype=dtype)
@@ -607,7 +607,7 @@ class CycleDiffusionPipeline(DiffusionPipeline):
 
         # 5. Prepare timesteps
         self.scheduler.set_timesteps(num_inference_steps, device=device)
-        timesteps = self.get_timesteps(num_inference_steps, strength, device)
+        timesteps, num_inference_steps = self.get_timesteps(num_inference_steps, strength, device)
         latent_timestep = timesteps[:1].repeat(batch_size * num_images_per_prompt)
 
         # 6. Prepare latent variables
@@ -621,7 +621,9 @@ class CycleDiffusionPipeline(DiffusionPipeline):
         generator = extra_step_kwargs.pop("generator", None)
 
         # 8. Denoising loop
-        for i, t in enumerate(self.progress_bar(timesteps)):
+        num_warmup_steps = len(timesteps) - num_inference_steps * self.scheduler.order
+        with self.progress_bar(total=num_inference_steps) as progress_bar:
+            for i, t in enumerate(timesteps):
                 # expand the latents if we are doing classifier free guidance
                 latent_model_input = torch.cat([latents] * 2)
                 source_latent_model_input = torch.cat([source_latents] * 2)
@@ -679,6 +681,8 @@ class CycleDiffusionPipeline(DiffusionPipeline):
                 ).prev_sample
 
                 # call the callback, if provided
+                if (i + 1) > num_warmup_steps and (i + 1) % self.scheduler.order == 0:
+                    progress_bar.update()
                     if callback is not None and i % callback_steps == 0:
                         callback(i, t, latents)
 

src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion.py

@@ -540,7 +540,9 @@ class StableDiffusionPipeline(DiffusionPipeline):
         extra_step_kwargs = self.prepare_extra_step_kwargs(generator, eta)
 
         # 7. Denoising loop
-        for i, t in enumerate(self.progress_bar(timesteps)):
+        num_warmup_steps = len(timesteps) - num_inference_steps * self.scheduler.order
+        with self.progress_bar(total=num_inference_steps) as progress_bar:
+            for i, t in enumerate(timesteps):
                 # expand the latents if we are doing classifier free guidance
                 latent_model_input = torch.cat([latents] * 2) if do_classifier_free_guidance else latents
                 latent_model_input = self.scheduler.scale_model_input(latent_model_input, t)
@@ -557,6 +559,8 @@ class StableDiffusionPipeline(DiffusionPipeline):
                     latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample
 
                 # call the callback, if provided
+                if (i + 1) > num_warmup_steps and (i + 1) % self.scheduler.order == 0:
+                    progress_bar.update()
                     if callback is not None and i % callback_steps == 0:
                         callback(i, t, latents)
 

src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_image_variation.py

@@ -441,7 +441,9 @@ class StableDiffusionImageVariationPipeline(DiffusionPipeline):
         extra_step_kwargs = self.prepare_extra_step_kwargs(generator, eta)
 
         # 7. Denoising loop
-        for i, t in enumerate(self.progress_bar(timesteps)):
+        num_warmup_steps = len(timesteps) - num_inference_steps * self.scheduler.order
+        with self.progress_bar(total=num_inference_steps) as progress_bar:
+            for i, t in enumerate(timesteps):
                 # expand the latents if we are doing classifier free guidance
                 latent_model_input = torch.cat([latents] * 2) if do_classifier_free_guidance else latents
                 latent_model_input = self.scheduler.scale_model_input(latent_model_input, t)
@@ -458,6 +460,8 @@ class StableDiffusionImageVariationPipeline(DiffusionPipeline):
                 latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample
 
                 # call the callback, if provided
+                if (i + 1) > num_warmup_steps and (i + 1) % self.scheduler.order == 0:
+                    progress_bar.update()
                     if callback is not None and i % callback_steps == 0:
                         callback(i, t, latents)
 

src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_img2img.py

@@ -442,7 +442,7 @@ class StableDiffusionImg2ImgPipeline(DiffusionPipeline):
         t_start = max(num_inference_steps - init_timestep + offset, 0)
         timesteps = self.scheduler.timesteps[t_start:]
 
-        return timesteps
+        return timesteps, num_inference_steps - t_start
 
     def prepare_latents(self, init_image, timestep, batch_size, num_images_per_prompt, dtype, device, generator=None):
         init_image = init_image.to(device=device, dtype=dtype)
@@ -571,7 +571,7 @@ class StableDiffusionImg2ImgPipeline(DiffusionPipeline):
 
         # 5. set timesteps
         self.scheduler.set_timesteps(num_inference_steps, device=device)
-        timesteps = self.get_timesteps(num_inference_steps, strength, device)
+        timesteps, num_inference_steps = self.get_timesteps(num_inference_steps, strength, device)
         latent_timestep = timesteps[:1].repeat(batch_size * num_images_per_prompt)
 
         # 6. Prepare latent variables
@@ -583,7 +583,9 @@ class StableDiffusionImg2ImgPipeline(DiffusionPipeline):
         extra_step_kwargs = self.prepare_extra_step_kwargs(generator, eta)
 
         # 8. Denoising loop
-        for i, t in enumerate(self.progress_bar(timesteps)):
+        num_warmup_steps = len(timesteps) - num_inference_steps * self.scheduler.order
+        with self.progress_bar(total=num_inference_steps) as progress_bar:
+            for i, t in enumerate(timesteps):
                 # expand the latents if we are doing classifier free guidance
                 latent_model_input = torch.cat([latents] * 2) if do_classifier_free_guidance else latents
                 latent_model_input = self.scheduler.scale_model_input(latent_model_input, t)
@@ -600,6 +602,8 @@ class StableDiffusionImg2ImgPipeline(DiffusionPipeline):
                 latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample
 
                 # call the callback, if provided
+                if (i + 1) > num_warmup_steps and (i + 1) % self.scheduler.order == 0:
+                    progress_bar.update()
                     if callback is not None and i % callback_steps == 0:
                         callback(i, t, latents)
 

src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_inpaint.py

@@ -655,7 +655,7 @@ class StableDiffusionInpaintPipeline(DiffusionPipeline):
 
         # 5. set timesteps
         self.scheduler.set_timesteps(num_inference_steps, device=device)
-        timesteps_tensor = self.scheduler.timesteps
+        timesteps = self.scheduler.timesteps
 
         # 6. Prepare latent variables
         num_channels_latents = self.vae.config.latent_channels
@@ -699,7 +699,9 @@ class StableDiffusionInpaintPipeline(DiffusionPipeline):
         extra_step_kwargs = self.prepare_extra_step_kwargs(generator, eta)
 
         # 10. Denoising loop
-        for i, t in enumerate(self.progress_bar(timesteps_tensor)):
+        num_warmup_steps = len(timesteps) - num_inference_steps * self.scheduler.order
+        with self.progress_bar(total=num_inference_steps) as progress_bar:
+            for i, t in enumerate(timesteps):
                 # expand the latents if we are doing classifier free guidance
                 latent_model_input = torch.cat([latents] * 2) if do_classifier_free_guidance else latents
 
@@ -719,6 +721,8 @@ class StableDiffusionInpaintPipeline(DiffusionPipeline):
                 latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample
 
                 # call the callback, if provided
+                if (i + 1) > num_warmup_steps and (i + 1) % self.scheduler.order == 0:
+                    progress_bar.update()
                     if callback is not None and i % callback_steps == 0:
                         callback(i, t, latents)
 

src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_inpaint_legacy.py

@@ -457,7 +457,7 @@ class StableDiffusionInpaintPipelineLegacy(DiffusionPipeline):
         t_start = max(num_inference_steps - init_timestep + offset, 0)
         timesteps = self.scheduler.timesteps[t_start:]
 
-        return timesteps
+        return timesteps, num_inference_steps - t_start
 
     def prepare_latents(self, init_image, timestep, batch_size, num_images_per_prompt, dtype, device, generator):
         init_image = init_image.to(device=self.device, dtype=dtype)
@@ -577,7 +577,7 @@ class StableDiffusionInpaintPipelineLegacy(DiffusionPipeline):
 
         # 5. set timesteps
         self.scheduler.set_timesteps(num_inference_steps, device=device)
-        timesteps = self.get_timesteps(num_inference_steps, strength, device)
+        timesteps, num_inference_steps = self.get_timesteps(num_inference_steps, strength, device)
         latent_timestep = timesteps[:1].repeat(batch_size * num_images_per_prompt)
 
         # 6. Prepare latent variables
@@ -594,7 +594,9 @@ class StableDiffusionInpaintPipelineLegacy(DiffusionPipeline):
         extra_step_kwargs = self.prepare_extra_step_kwargs(generator, eta)
 
         # 9. Denoising loop
-        for i, t in enumerate(self.progress_bar(timesteps)):
+        num_warmup_steps = len(timesteps) - num_inference_steps * self.scheduler.order
+        with self.progress_bar(total=num_inference_steps) as progress_bar:
+            for i, t in enumerate(timesteps):
                 # expand the latents if we are doing classifier free guidance
                 latent_model_input = torch.cat([latents] * 2) if do_classifier_free_guidance else latents
                 latent_model_input = self.scheduler.scale_model_input(latent_model_input, t)
@@ -615,6 +617,8 @@ class StableDiffusionInpaintPipelineLegacy(DiffusionPipeline):
                 latents = (init_latents_proper * mask) + (latents * (1 - mask))
 
                 # call the callback, if provided
+                if (i + 1) > num_warmup_steps and (i + 1) % self.scheduler.order == 0:
+                    progress_bar.update()
                     if callback is not None and i % callback_steps == 0:
                         callback(i, t, latents)
 

src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_upscale.py

@@ -469,7 +469,7 @@ class StableDiffusionUpscalePipeline(DiffusionPipeline):
 
         # 5. set timesteps
         self.scheduler.set_timesteps(num_inference_steps, device=device)
-        timesteps_tensor = self.scheduler.timesteps
+        timesteps = self.scheduler.timesteps
 
         # 5. Add noise to image
         noise_level = torch.tensor([noise_level], dtype=torch.long, device=device)
@@ -511,7 +511,9 @@ class StableDiffusionUpscalePipeline(DiffusionPipeline):
         extra_step_kwargs = self.prepare_extra_step_kwargs(generator, eta)
 
         # 9. Denoising loop
-        for i, t in enumerate(self.progress_bar(timesteps_tensor)):
+        num_warmup_steps = len(timesteps) - num_inference_steps * self.scheduler.order
+        with self.progress_bar(total=num_inference_steps) as progress_bar:
+            for i, t in enumerate(timesteps):
                 # expand the latents if we are doing classifier free guidance
                 latent_model_input = torch.cat([latents] * 2) if do_classifier_free_guidance else latents
 
@@ -533,6 +535,8 @@ class StableDiffusionUpscalePipeline(DiffusionPipeline):
                 latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample
 
                 # call the callback, if provided
+                if (i + 1) > num_warmup_steps and (i + 1) % self.scheduler.order == 0:
+                    progress_bar.update()
                     if callback is not None and i % callback_steps == 0:
                         callback(i, t, latents)
 

src/diffusers/pipelines/stable_diffusion_safe/pipeline_stable_diffusion_safe.py

@@ -668,10 +668,14 @@ class StableDiffusionPipelineSafe(DiffusionPipeline):
 
         safety_momentum = None
 
-        for i, t in enumerate(self.progress_bar(timesteps)):
+        num_warmup_steps = len(timesteps) - num_inference_steps * self.scheduler.order
+        with self.progress_bar(total=num_inference_steps) as progress_bar:
+            for i, t in enumerate(timesteps):
                 # expand the latents if we are doing classifier free guidance
                 latent_model_input = (
-                torch.cat([latents] * (3 if enable_safety_guidance else 2)) if do_classifier_free_guidance else latents
+                    torch.cat([latents] * (3 if enable_safety_guidance else 2))
+                    if do_classifier_free_guidance
+                    else latents
                 )
                 latent_model_input = self.scheduler.scale_model_input(latent_model_input, t)
 
@@ -699,7 +703,9 @@ class StableDiffusionPipelineSafe(DiffusionPipeline):
 
                         # Equation 6
                         safety_concept_scale = torch.where(
-                        (noise_pred_text - noise_pred_safety_concept) >= sld_threshold, torch.zeros_like(scale), scale
+                            (noise_pred_text - noise_pred_safety_concept) >= sld_threshold,
+                            torch.zeros_like(scale),
+                            scale,
                         )
 
                         # Equation 4
@@ -723,6 +729,8 @@ class StableDiffusionPipelineSafe(DiffusionPipeline):
                 latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample
 
                 # call the callback, if provided
+                if (i + 1) > num_warmup_steps and (i + 1) % self.scheduler.order == 0:
+                    progress_bar.update()
                     if callback is not None and i % callback_steps == 0:
                         callback(i, t, latents)
 

src/diffusers/schedulers/__init__.py

@@ -22,6 +22,7 @@ if is_torch_available():
     from .scheduling_dpmsolver_multistep import DPMSolverMultistepScheduler
     from .scheduling_euler_ancestral_discrete import EulerAncestralDiscreteScheduler
     from .scheduling_euler_discrete import EulerDiscreteScheduler
+    from .scheduling_heun import HeunDiscreteScheduler
     from .scheduling_ipndm import IPNDMScheduler
     from .scheduling_karras_ve import KarrasVeScheduler
     from .scheduling_pndm import PNDMScheduler

src/diffusers/schedulers/scheduling_ddim.py

@@ -114,6 +114,7 @@ class DDIMScheduler(SchedulerMixin, ConfigMixin):
 
     _compatibles = _COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS.copy()
     _deprecated_kwargs = ["predict_epsilon"]
+    order = 1
 
     @register_to_config
     def __init__(

src/diffusers/schedulers/scheduling_ddpm.py

@@ -106,6 +106,7 @@ class DDPMScheduler(SchedulerMixin, ConfigMixin):
 
     _compatibles = _COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS.copy()
     _deprecated_kwargs = ["predict_epsilon"]
+    order = 1
 
     @register_to_config
     def __init__(

src/diffusers/schedulers/scheduling_dpmsolver_multistep.py

@@ -118,6 +118,7 @@ class DPMSolverMultistepScheduler(SchedulerMixin, ConfigMixin):
 
     _compatibles = _COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS.copy()
     _deprecated_kwargs = ["predict_epsilon"]
+    order = 1
 
     @register_to_config
     def __init__(

src/diffusers/schedulers/scheduling_euler_ancestral_discrete.py

@@ -68,6 +68,7 @@ class EulerAncestralDiscreteScheduler(SchedulerMixin, ConfigMixin):
     """
 
     _compatibles = _COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS.copy()
+    order = 1
 
     @register_to_config
     def __init__(

src/diffusers/schedulers/scheduling_euler_discrete.py

@@ -69,6 +69,7 @@ class EulerDiscreteScheduler(SchedulerMixin, ConfigMixin):
     """
 
     _compatibles = _COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS.copy()
+    order = 1
 
     @register_to_config
     def __init__(

src/diffusers/schedulers/scheduling_heun.py

+# Copyright 2022 Katherine Crowson, The HuggingFace Team and hlky. All rights reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+from typing import Optional, Tuple, Union
+
+import numpy as np
+import torch
+
+from ..configuration_utils import ConfigMixin, register_to_config
+from ..utils import _COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS
+from .scheduling_utils import SchedulerMixin, SchedulerOutput
+
+
+class HeunDiscreteScheduler(SchedulerMixin, ConfigMixin):
+    """
+    Args:
+    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
+    [`~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`.
+    [`~ConfigMixin`] also provides general loading and saving functionality via the [`~ConfigMixin.save_config`] and
+    [`~ConfigMixin.from_config`] functions.
+        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):
+            option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
+            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`.
+        tensor_format (`str`): whether the scheduler expects pytorch or numpy arrays.
+    """
+
+    _compatibles = _COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS.copy()
+    order = 2
+
+    @register_to_config
+    def __init__(
+        self,
+        num_train_timesteps: int = 1000,
+        beta_start: float = 0.00085,  # sensible defaults
+        beta_end: float = 0.012,
+        beta_schedule: str = "linear",
+        trained_betas: Optional[np.ndarray] = None,
+    ):
+        if trained_betas is not None:
+            self.betas = torch.from_numpy(trained_betas)
+        elif beta_schedule == "linear":
+            self.betas = torch.linspace(beta_start, beta_end, num_train_timesteps, dtype=torch.float32)
+        elif beta_schedule == "scaled_linear":
+            # this schedule is very specific to the latent diffusion model.
+            self.betas = (
+                torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2
+            )
+        else:
+            raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}")
+
+        self.alphas = 1.0 - self.betas
+        self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
+
+        #  set all values
+        self.set_timesteps(num_train_timesteps, None, num_train_timesteps)
+
+    def index_for_timestep(self, timestep):
+        indices = (self.timesteps == timestep).nonzero()
+        if self.state_in_first_order:
+            pos = 0 if indices.shape[0] < 2 else 1
+        else:
+            pos = 0
+        return indices[pos].item()
+
+    def scale_model_input(
+        self,
+        sample: torch.FloatTensor,
+        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
+        Returns:
+            `torch.FloatTensor`: scaled input sample
+        """
+        step_index = self.index_for_timestep(timestep)
+
+        sigma = self.sigmas[step_index]
+        sample = sample / ((sigma**2 + 1) ** 0.5)
+        return sample
+
+    def set_timesteps(
+        self,
+        num_inference_steps: int,
+        device: Union[str, torch.device] = None,
+        num_train_timesteps: Optional[int] = None,
+    ):
+        """
+        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.
+            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
+
+        num_train_timesteps = num_train_timesteps or self.config.num_train_timesteps
+
+        timesteps = np.linspace(0, num_train_timesteps - 1, num_inference_steps, dtype=float)[::-1].copy()
+
+        sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
+        sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
+        sigmas = np.concatenate([sigmas, [0.0]]).astype(np.float32)
+        sigmas = torch.from_numpy(sigmas).to(device=device)
+        self.sigmas = torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2), sigmas[-1:]])
+
+        # standard deviation of the initial noise distribution
+        self.init_noise_sigma = self.sigmas.max()
+
+        timesteps = torch.from_numpy(timesteps)
+        timesteps = torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2), timesteps[-1:]])
+
+        if str(device).startswith("mps"):
+            # mps does not support float64
+            self.timesteps = timesteps.to(device, dtype=torch.float32)
+        else:
+            self.timesteps = timesteps.to(device=device)
+
+        # empty dt and derivative
+        self.prev_derivative = None
+        self.dt = None
+
+    @property
+    def state_in_first_order(self):
+        return self.dt is None
+
+    def step(
+        self,
+        model_output: Union[torch.FloatTensor, np.ndarray],
+        timestep: Union[float, torch.FloatTensor],
+        sample: Union[torch.FloatTensor, np.ndarray],
+        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
+        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
+        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.
+        """
+        step_index = self.index_for_timestep(timestep)
+
+        if self.state_in_first_order:
+            sigma = self.sigmas[step_index]
+            sigma_next = self.sigmas[step_index + 1]
+        else:
+            # 2nd order / Heun's method
+            sigma = self.sigmas[step_index - 1]
+            sigma_next = self.sigmas[step_index]
+
+        # currently only gamma=0 is supported. This usually works best anyways.
+        # We can support gamma in the future but then need to scale the timestep before
+        # passing it to the model which requires a change in API
+        gamma = 0
+        sigma_hat = sigma * (gamma + 1)  # Note: sigma_hat == sigma for now
+
+        # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
+        pred_original_sample = sample - sigma_hat * model_output
+
+        if self.state_in_first_order:
+            # 2. Convert to an ODE derivative
+            derivative = (sample - pred_original_sample) / sigma_hat
+            # 3. 1st order derivative
+            dt = sigma_next - sigma_hat
+
+            # store for 2nd order step
+            self.prev_derivative = derivative
+            self.dt = dt
+            self.sample = sample
+        else:
+            # 2. 2nd order / Heun's method
+            derivative = (sample - pred_original_sample) / sigma_hat
+            derivative = (self.prev_derivative + derivative) / 2
+
+            # 3. Retrieve 1st order derivative
+            dt = self.dt
+            sample = self.sample
+
+            # free dt and derivative
+            # Note, this puts the scheduler in "first order mode"
+            self.prev_derivative = None
+            self.dt = None
+            self.sample = None
+
+        prev_sample = sample + derivative * dt
+
+        if not return_dict:
+            return (prev_sample,)
+
+        return SchedulerOutput(prev_sample=prev_sample)
+
+    def add_noise(
+        self,
+        original_samples: torch.FloatTensor,
+        noise: torch.FloatTensor,
+        timesteps: torch.FloatTensor,
+    ) -> torch.FloatTensor:
+        # Make sure sigmas and timesteps have the same device and dtype as original_samples
+        self.sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
+        if original_samples.device.type == "mps" and torch.is_floating_point(timesteps):
+            # mps does not support float64
+            self.timesteps = self.timesteps.to(original_samples.device, dtype=torch.float32)
+            timesteps = timesteps.to(original_samples.device, dtype=torch.float32)
+        else:
+            self.timesteps = self.timesteps.to(original_samples.device)
+            timesteps = timesteps.to(original_samples.device)
+
+        step_indices = [self.index_for_timestep(t) for t in timesteps]
+
+        sigma = self.sigmas[step_indices].flatten()
+        while len(sigma.shape) < len(original_samples.shape):
+            sigma = sigma.unsqueeze(-1)
+
+        noisy_samples = original_samples + noise * sigma
+        return noisy_samples
+
+    def __len__(self):
+        return self.config.num_train_timesteps

src/diffusers/schedulers/scheduling_ipndm.py

@@ -37,6 +37,8 @@ class IPNDMScheduler(SchedulerMixin, ConfigMixin):
         num_train_timesteps (`int`): number of diffusion steps used to train the model.
     """
 
+    order = 1
+
     @register_to_config
     def __init__(self, num_train_timesteps: int = 1000):
         # set `betas`, `alphas`, `timesteps`