feat : add log-rho deis multistep scheduler (#1432)

* feat : add log-rho deis multistep deis

* docs :fix typo

* docs : add docs for impl algo

* docs : remove duplicate ref

* finish deis

* add docs

* fix
Co-authored-by: Patrick von Platen <patrick.v.platen@gmail.com>

docs/source/en/_toctree.yml

@@ -155,6 +155,8 @@
       title: "DDIM"
     - local: api/schedulers/ddpm
       title: "DDPM"
+    - local: api/schedulers/deis
+      title: "DEIS"
     - local: api/schedulers/singlestep_dpm_solver
       title: "Singlestep DPM-Solver"
     - local: api/schedulers/multistep_dpm_solver

docs/source/en/api/schedulers/deis.mdx

+<!--Copyright 2022 The HuggingFace Team. 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.
+-->
+
+# DEIS
+
+Fast Sampling of Diffusion Models with Exponential Integrator.
+
+## Overview
+
+Original paper can be found [here](https://arxiv.org/abs/2204.13902). The original implementation can be found [here](https://github.com/qsh-zh/deis).
+
+## DEISMultistepScheduler
+[[autodoc]] DEISMultistepScheduler

src/diffusers/__init__.py

@@ -67,6 +67,7 @@ else:
     from .schedulers import (
         DDIMScheduler,
         DDPMScheduler,
+        DEISMultistepScheduler,
         DPMSolverMultistepScheduler,
         DPMSolverSinglestepScheduler,
         EulerAncestralDiscreteScheduler,

src/diffusers/schedulers/__init__.py

@@ -24,6 +24,7 @@ except OptionalDependencyNotAvailable:
 else:
     from .scheduling_ddim import DDIMScheduler
     from .scheduling_ddpm import DDPMScheduler
+    from .scheduling_deis_multistep import DEISMultistepScheduler
     from .scheduling_dpmsolver_multistep import DPMSolverMultistepScheduler
     from .scheduling_dpmsolver_singlestep import DPMSolverSinglestepScheduler
     from .scheduling_euler_ancestral_discrete import EulerAncestralDiscreteScheduler

src/diffusers/schedulers/scheduling_deis_multistep.py

+# Copyright 2022 FLAIR Lab and The HuggingFace Team. 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.
+
+# DISCLAIMER: check https://arxiv.org/abs/2204.13902 and https://github.com/qsh-zh/deis for more info
+# The codebase is modified based on https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_dpmsolver_multistep.py
+
+import math
+from typing import List, 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
+
+
+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].
+
+    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):
+        return math.cos((time_step + 0.008) / 1.008 * math.pi / 2) ** 2
+
+    betas = []
+    for i in range(num_diffusion_timesteps):
+        t1 = i / num_diffusion_timesteps
+        t2 = (i + 1) / num_diffusion_timesteps
+        betas.append(min(1 - alpha_bar(t2) / alpha_bar(t1), max_beta))
+    return torch.tensor(betas, dtype=torch.float32)
+
+
+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.
+
+    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.
+
+    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):
+            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 woks 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.
+
+    """
+
+    _compatibles = _COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS.copy()
+    order = 1
+
+    @register_to_config
+    def __init__(
+        self,
+        num_train_timesteps: int = 1000,
+        beta_start: float = 0.0001,
+        beta_end: float = 0.02,
+        beta_schedule: str = "linear",
+        trained_betas: Optional[np.ndarray] = None,
+        solver_order: int = 2,
+        prediction_type: str = "epsilon",
+        thresholding: bool = False,
+        dynamic_thresholding_ratio: float = 0.995,
+        sample_max_value: float = 1.0,
+        algorithm_type: str = "deis",
+        solver_type: str = "logrho",
+        lower_order_final: bool = True,
+    ):
+        if trained_betas is not None:
+            self.betas = torch.tensor(trained_betas, dtype=torch.float32)
+        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
+            )
+        elif beta_schedule == "squaredcos_cap_v2":
+            # Glide cosine schedule
+            self.betas = betas_for_alpha_bar(num_train_timesteps)
+        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)
+        # Currently we only support VP-type noise schedule
+        self.alpha_t = torch.sqrt(self.alphas_cumprod)
+        self.sigma_t = torch.sqrt(1 - self.alphas_cumprod)
+        self.lambda_t = torch.log(self.alpha_t) - torch.log(self.sigma_t)
+
+        # standard deviation of the initial noise distribution
+        self.init_noise_sigma = 1.0
+
+        # settings for DEIS
+        if algorithm_type not in ["deis"]:
+            if algorithm_type in ["dpmsolver", "dpmsolver++"]:
+                algorithm_type = "deis"
+            else:
+                raise NotImplementedError(f"{algorithm_type} does is not implemented for {self.__class__}")
+
+        if solver_type not in ["logrho"]:
+            if solver_type in ["midpoint", "heun"]:
+                solver_type = "logrho"
+            else:
+                raise NotImplementedError(f"solver type {solver_type} does is not implemented for {self.__class__}")
+
+        # setable values
+        self.num_inference_steps = None
+        timesteps = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=np.float32)[::-1].copy()
+        self.timesteps = torch.from_numpy(timesteps)
+        self.model_outputs = [None] * solver_order
+        self.lower_order_nums = 0
+
+    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.
+
+        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
+        timesteps = (
+            np.linspace(0, self.num_train_timesteps - 1, num_inference_steps + 1)
+            .round()[::-1][:-1]
+            .copy()
+            .astype(np.int64)
+        )
+        self.timesteps = torch.from_numpy(timesteps).to(device)
+        self.model_outputs = [
+            None,
+        ] * self.config.solver_order
+        self.lower_order_nums = 0
+
+    def convert_model_output(
+        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.
+
+        Args:
+            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
+            timestep (`int`): current discrete timestep in the diffusion chain.
+            sample (`torch.FloatTensor`):
+                current instance of sample being created by diffusion process.
+
+        Returns:
+            `torch.FloatTensor`: the converted model output.
+        """
+        if self.config.prediction_type == "epsilon":
+            alpha_t, sigma_t = self.alpha_t[timestep], self.sigma_t[timestep]
+            x0_pred = (sample - sigma_t * model_output) / alpha_t
+        elif self.config.prediction_type == "sample":
+            x0_pred = model_output
+        elif self.config.prediction_type == "v_prediction":
+            alpha_t, sigma_t = self.alpha_t[timestep], self.sigma_t[timestep]
+            x0_pred = alpha_t * sample - sigma_t * model_output
+        else:
+            raise ValueError(
+                f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
+                " `v_prediction` for the DEISMultistepScheduler."
+            )
+
+        if self.config.thresholding:
+            # Dynamic thresholding in https://arxiv.org/abs/2205.11487
+            orig_dtype = x0_pred.dtype
+            if orig_dtype not in [torch.float, torch.double]:
+                x0_pred = x0_pred.float()
+            dynamic_max_val = torch.quantile(
+                torch.abs(x0_pred).reshape((x0_pred.shape[0], -1)), self.config.dynamic_thresholding_ratio, dim=1
+            )
+            dynamic_max_val = torch.maximum(
+                dynamic_max_val,
+                self.config.sample_max_value * torch.ones_like(dynamic_max_val).to(dynamic_max_val.device),
+            )[(...,) + (None,) * (x0_pred.ndim - 1)]
+            x0_pred = torch.clamp(x0_pred, -dynamic_max_val, dynamic_max_val) / dynamic_max_val
+            x0_pred = x0_pred.type(orig_dtype)
+
+        if self.config.algorithm_type == "deis":
+            alpha_t, sigma_t = self.alpha_t[timestep], self.sigma_t[timestep]
+            return (sample - alpha_t * x0_pred) / sigma_t
+        else:
+            raise NotImplementedError("only support log-rho multistep deis now")
+
+    def deis_first_order_update(
+        self,
+        model_output: torch.FloatTensor,
+        timestep: int,
+        prev_timestep: int,
+        sample: torch.FloatTensor,
+    ) -> torch.FloatTensor:
+        """
+        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.
+            sample (`torch.FloatTensor`):
+                current instance of sample being created by diffusion process.
+
+        Returns:
+            `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]
+        sigma_t, _ = self.sigma_t[prev_timestep], self.sigma_t[timestep]
+        h = lambda_t - lambda_s
+        if self.config.algorithm_type == "deis":
+            x_t = (alpha_t / alpha_s) * sample - (sigma_t * (torch.exp(h) - 1.0)) * model_output
+        else:
+            raise NotImplementedError("only support log-rho multistep deis now")
+        return x_t
+
+    def multistep_deis_second_order_update(
+        self,
+        model_output_list: List[torch.FloatTensor],
+        timestep_list: List[int],
+        prev_timestep: int,
+        sample: torch.FloatTensor,
+    ) -> torch.FloatTensor:
+        """
+        One step for the second-order multistep DEIS.
+
+        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.
+            sample (`torch.FloatTensor`):
+                current instance of sample being created by diffusion process.
+
+        Returns:
+            `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]
+        alpha_t, alpha_s0, alpha_s1 = self.alpha_t[t], self.alpha_t[s0], self.alpha_t[s1]
+        sigma_t, sigma_s0, sigma_s1 = self.sigma_t[t], self.sigma_t[s0], self.sigma_t[s1]
+
+        rho_t, rho_s0, rho_s1 = sigma_t / alpha_t, sigma_s0 / alpha_s0, sigma_s1 / alpha_s1
+
+        if self.config.algorithm_type == "deis":
+
+            def ind_fn(t, b, c):
+                # Integrate[(log(t) - log(c)) / (log(b) - log(c)), {t}]
+                return t * (-np.log(c) + np.log(t) - 1) / (np.log(b) - np.log(c))
+
+            coef1 = ind_fn(rho_t, rho_s0, rho_s1) - ind_fn(rho_s0, rho_s0, rho_s1)
+            coef2 = ind_fn(rho_t, rho_s1, rho_s0) - ind_fn(rho_s0, rho_s1, rho_s0)
+
+            x_t = alpha_t * (sample / alpha_s0 + coef1 * m0 + coef2 * m1)
+            return x_t
+        else:
+            raise NotImplementedError("only support log-rho multistep deis now")
+
+    def multistep_deis_third_order_update(
+        self,
+        model_output_list: List[torch.FloatTensor],
+        timestep_list: List[int],
+        prev_timestep: int,
+        sample: torch.FloatTensor,
+    ) -> torch.FloatTensor:
+        """
+        One step for the third-order multistep DEIS.
+
+        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.
+            sample (`torch.FloatTensor`):
+                current instance of sample being created by diffusion process.
+
+        Returns:
+            `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]
+        alpha_t, alpha_s0, alpha_s1, alpha_s2 = self.alpha_t[t], self.alpha_t[s0], self.alpha_t[s1], self.alpha_t[s2]
+        sigma_t, sigma_s0, sigma_s1, simga_s2 = self.sigma_t[t], self.sigma_t[s0], self.sigma_t[s1], self.sigma_t[s2]
+        rho_t, rho_s0, rho_s1, rho_s2 = (
+            sigma_t / alpha_t,
+            sigma_s0 / alpha_s0,
+            sigma_s1 / alpha_s1,
+            simga_s2 / alpha_s2,
+        )
+
+        if self.config.algorithm_type == "deis":
+
+            def ind_fn(t, b, c, d):
+                # Integrate[(log(t) - log(c))(log(t) - log(d)) / (log(b) - log(c))(log(b) - log(d)), {t}]
+                numerator = t * (
+                    np.log(c) * (np.log(d) - np.log(t) + 1)
+                    - np.log(d) * np.log(t)
+                    + np.log(d)
+                    + np.log(t) ** 2
+                    - 2 * np.log(t)
+                    + 2
+                )
+                denominator = (np.log(b) - np.log(c)) * (np.log(b) - np.log(d))
+                return numerator / denominator
+
+            coef1 = ind_fn(rho_t, rho_s0, rho_s1, rho_s2) - ind_fn(rho_s0, rho_s0, rho_s1, rho_s2)
+            coef2 = ind_fn(rho_t, rho_s1, rho_s2, rho_s0) - ind_fn(rho_s0, rho_s1, rho_s2, rho_s0)
+            coef3 = ind_fn(rho_t, rho_s2, rho_s0, rho_s1) - ind_fn(rho_s0, rho_s2, rho_s0, rho_s1)
+
+            x_t = alpha_t * (sample / alpha_s0 + coef1 * m0 + coef2 * m1 + coef3 * m2)
+
+            return x_t
+        else:
+            raise NotImplementedError("only support log-rho multistep deis now")
+
+    def step(
+        self,
+        model_output: torch.FloatTensor,
+        timestep: int,
+        sample: torch.FloatTensor,
+        return_dict: bool = True,
+    ) -> Union[SchedulerOutput, Tuple]:
+        """
+        Step function propagating 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.
+            sample (`torch.FloatTensor`):
+                current instance of sample being created by diffusion process.
+            return_dict (`bool`): option for returning tuple rather than SchedulerOutput class
+
+        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.
+
+        """
+        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"
+            )
+
+        if isinstance(timestep, torch.Tensor):
+            timestep = timestep.to(self.timesteps.device)
+        step_index = (self.timesteps == timestep).nonzero()
+        if len(step_index) == 0:
+            step_index = len(self.timesteps) - 1
+        else:
+            step_index = step_index.item()
+        prev_timestep = 0 if step_index == len(self.timesteps) - 1 else self.timesteps[step_index + 1]
+        lower_order_final = (
+            (step_index == len(self.timesteps) - 1) and self.config.lower_order_final and len(self.timesteps) < 15
+        )
+        lower_order_second = (
+            (step_index == len(self.timesteps) - 2) and self.config.lower_order_final and len(self.timesteps) < 15
+        )
+
+        model_output = self.convert_model_output(model_output, timestep, sample)
+        for i in range(self.config.solver_order - 1):
+            self.model_outputs[i] = self.model_outputs[i + 1]
+        self.model_outputs[-1] = model_output
+
+        if self.config.solver_order == 1 or self.lower_order_nums < 1 or lower_order_final:
+            prev_sample = self.deis_first_order_update(model_output, timestep, prev_timestep, sample)
+        elif self.config.solver_order == 2 or self.lower_order_nums < 2 or lower_order_second:
+            timestep_list = [self.timesteps[step_index - 1], timestep]
+            prev_sample = self.multistep_deis_second_order_update(
+                self.model_outputs, timestep_list, prev_timestep, sample
+            )
+        else:
+            timestep_list = [self.timesteps[step_index - 2], self.timesteps[step_index - 1], timestep]
+            prev_sample = self.multistep_deis_third_order_update(
+                self.model_outputs, timestep_list, prev_timestep, sample
+            )
+
+        if self.lower_order_nums < self.config.solver_order:
+            self.lower_order_nums += 1
+
+        if not return_dict:
+            return (prev_sample,)
+
+        return SchedulerOutput(prev_sample=prev_sample)
+
+    def scale_model_input(self, sample: torch.FloatTensor, *args, **kwargs) -> torch.FloatTensor:
+        """
+        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
+        current timestep.
+
+        Args:
+            sample (`torch.FloatTensor`): input sample
+
+        Returns:
+            `torch.FloatTensor`: scaled input sample
+        """
+        return sample
+
+    def add_noise(
+        self,
+        original_samples: torch.FloatTensor,
+        noise: torch.FloatTensor,
+        timesteps: torch.IntTensor,
+    ) -> torch.FloatTensor:
+        # Make sure alphas_cumprod and timestep have same device and dtype as original_samples
+        self.alphas_cumprod = self.alphas_cumprod.to(device=original_samples.device, dtype=original_samples.dtype)
+        timesteps = timesteps.to(original_samples.device)
+
+        sqrt_alpha_prod = self.alphas_cumprod[timesteps] ** 0.5
+        sqrt_alpha_prod = sqrt_alpha_prod.flatten()
+        while len(sqrt_alpha_prod.shape) < len(original_samples.shape):
+            sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)
+
+        sqrt_one_minus_alpha_prod = (1 - self.alphas_cumprod[timesteps]) ** 0.5
+        sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten()
+        while len(sqrt_one_minus_alpha_prod.shape) < len(original_samples.shape):
+            sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)
+
+        noisy_samples = sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
+        return noisy_samples
+
+    def __len__(self):
+        return self.config.num_train_timesteps

src/diffusers/schedulers/scheduling_dpmsolver_multistep.py

@@ -174,9 +174,15 @@ class DPMSolverMultistepScheduler(SchedulerMixin, ConfigMixin):
 
         # settings for DPM-Solver
         if algorithm_type not in ["dpmsolver", "dpmsolver++"]:
-            raise NotImplementedError(f"{algorithm_type} does is not implemented for {self.__class__}")
+            if algorithm_type == "deis":
+                algorithm_type = "dpmsolver++"
+            else:
+                raise NotImplementedError(f"{algorithm_type} does is not implemented for {self.__class__}")
         if solver_type not in ["midpoint", "heun"]:
-            raise NotImplementedError(f"{solver_type} does is not implemented for {self.__class__}")
+            if solver_type == "logrho":
+                solver_type = "midpoint"
+            else:
+                raise NotImplementedError(f"{solver_type} does is not implemented for {self.__class__}")
 
         # setable values
         self.num_inference_steps = None

src/diffusers/schedulers/scheduling_dpmsolver_singlestep.py

@@ -163,9 +163,15 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
 
         # settings for DPM-Solver
         if algorithm_type not in ["dpmsolver", "dpmsolver++"]:
-            raise NotImplementedError(f"{algorithm_type} does is not implemented for {self.__class__}")
+            if algorithm_type == "deis":
+                algorithm_type = "dpmsolver++"
+            else:
+                raise NotImplementedError(f"{algorithm_type} does is not implemented for {self.__class__}")
         if solver_type not in ["midpoint", "heun"]:
-            raise NotImplementedError(f"{solver_type} does is not implemented for {self.__class__}")
+            if solver_type == "logrho":
+                solver_type = "midpoint"
+            else:
+                raise NotImplementedError(f"{solver_type} does is not implemented for {self.__class__}")
 
         # setable values
         self.num_inference_steps = None

src/diffusers/utils/constants.py

@@ -41,4 +41,7 @@ _COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS = [
     "EulerAncestralDiscreteScheduler",
     "DPMSolverMultistepScheduler",
     "DPMSolverSinglestepScheduler",
+    "KDPM2DiscreteScheduler",
+    "KDPM2AncestralDiscreteScheduler",
+    "DEISMultistepScheduler",
 ]

src/diffusers/utils/dummy_pt_objects.py

@@ -362,6 +362,21 @@ class DDPMScheduler(metaclass=DummyObject):
         requires_backends(cls, ["torch"])
 
 
+class DEISMultistepScheduler(metaclass=DummyObject):
+    _backends = ["torch"]
+
+    def __init__(self, *args, **kwargs):
+        requires_backends(self, ["torch"])
+
+    @classmethod
+    def from_config(cls, *args, **kwargs):
+        requires_backends(cls, ["torch"])
+
+    @classmethod
+    def from_pretrained(cls, *args, **kwargs):
+        requires_backends(cls, ["torch"])
+
+
 class DPMSolverMultistepScheduler(metaclass=DummyObject):
     _backends = ["torch"]
 

tests/test_scheduler.py

@@ -27,6 +27,7 @@ import diffusers
 from diffusers import (
     DDIMScheduler,
     DDPMScheduler,
+    DEISMultistepScheduler,
     DPMSolverMultistepScheduler,
     DPMSolverSinglestepScheduler,
     EulerAncestralDiscreteScheduler,
@@ -2505,6 +2506,207 @@ class KDPM2DiscreteSchedulerTest(SchedulerCommonTest):
             assert abs(result_mean.item() - 0.0266) < 1e-3
 
 
+class DEISMultistepSchedulerTest(SchedulerCommonTest):
+    scheduler_classes = (DEISMultistepScheduler,)
+    forward_default_kwargs = (("num_inference_steps", 25),)
+
+    def get_scheduler_config(self, **kwargs):
+        config = {
+            "num_train_timesteps": 1000,
+            "beta_start": 0.0001,
+            "beta_end": 0.02,
+            "beta_schedule": "linear",
+            "solver_order": 2,
+        }
+
+        config.update(**kwargs)
+        return config
+
+    def check_over_configs(self, time_step=0, **config):
+        kwargs = dict(self.forward_default_kwargs)
+        num_inference_steps = kwargs.pop("num_inference_steps", None)
+        sample = self.dummy_sample
+        residual = 0.1 * sample
+        dummy_past_residuals = [residual + 0.2, residual + 0.15, residual + 0.10]
+
+        for scheduler_class in self.scheduler_classes:
+            scheduler_config = self.get_scheduler_config(**config)
+            scheduler = scheduler_class(**scheduler_config)
+            scheduler.set_timesteps(num_inference_steps)
+            # copy over dummy past residuals
+            scheduler.model_outputs = dummy_past_residuals[: scheduler.config.solver_order]
+
+            with tempfile.TemporaryDirectory() as tmpdirname:
+                scheduler.save_config(tmpdirname)
+                new_scheduler = scheduler_class.from_pretrained(tmpdirname)
+                new_scheduler.set_timesteps(num_inference_steps)
+                # copy over dummy past residuals
+                new_scheduler.model_outputs = dummy_past_residuals[: new_scheduler.config.solver_order]
+
+            output, new_output = sample, sample
+            for t in range(time_step, time_step + scheduler.config.solver_order + 1):
+                output = scheduler.step(residual, t, output, **kwargs).prev_sample
+                new_output = new_scheduler.step(residual, t, new_output, **kwargs).prev_sample
+
+                assert torch.sum(torch.abs(output - new_output)) < 1e-5, "Scheduler outputs are not identical"
+
+    def test_from_save_pretrained(self):
+        pass
+
+    def check_over_forward(self, time_step=0, **forward_kwargs):
+        kwargs = dict(self.forward_default_kwargs)
+        num_inference_steps = kwargs.pop("num_inference_steps", None)
+        sample = self.dummy_sample
+        residual = 0.1 * sample
+        dummy_past_residuals = [residual + 0.2, residual + 0.15, residual + 0.10]
+
+        for scheduler_class in self.scheduler_classes:
+            scheduler_config = self.get_scheduler_config()
+            scheduler = scheduler_class(**scheduler_config)
+            scheduler.set_timesteps(num_inference_steps)
+
+            # copy over dummy past residuals (must be after setting timesteps)
+            scheduler.model_outputs = dummy_past_residuals[: scheduler.config.solver_order]
+
+            with tempfile.TemporaryDirectory() as tmpdirname:
+                scheduler.save_config(tmpdirname)
+                new_scheduler = scheduler_class.from_pretrained(tmpdirname)
+                # copy over dummy past residuals
+                new_scheduler.set_timesteps(num_inference_steps)
+
+                # copy over dummy past residual (must be after setting timesteps)
+                new_scheduler.model_outputs = dummy_past_residuals[: new_scheduler.config.solver_order]
+
+            output = scheduler.step(residual, time_step, sample, **kwargs).prev_sample
+            new_output = new_scheduler.step(residual, time_step, sample, **kwargs).prev_sample
+
+            assert torch.sum(torch.abs(output - new_output)) < 1e-5, "Scheduler outputs are not identical"
+
+    def full_loop(self, **config):
+        scheduler_class = self.scheduler_classes[0]
+        scheduler_config = self.get_scheduler_config(**config)
+        scheduler = scheduler_class(**scheduler_config)
+
+        num_inference_steps = 10
+        model = self.dummy_model()
+        sample = self.dummy_sample_deter
+        scheduler.set_timesteps(num_inference_steps)
+
+        for i, t in enumerate(scheduler.timesteps):
+            residual = model(sample, t)
+            sample = scheduler.step(residual, t, sample).prev_sample
+
+        return sample
+
+    def test_step_shape(self):
+        kwargs = dict(self.forward_default_kwargs)
+
+        num_inference_steps = kwargs.pop("num_inference_steps", None)
+
+        for scheduler_class in self.scheduler_classes:
+            scheduler_config = self.get_scheduler_config()
+            scheduler = scheduler_class(**scheduler_config)
+
+            sample = self.dummy_sample
+            residual = 0.1 * sample
+
+            if num_inference_steps is not None and hasattr(scheduler, "set_timesteps"):
+                scheduler.set_timesteps(num_inference_steps)
+            elif num_inference_steps is not None and not hasattr(scheduler, "set_timesteps"):
+                kwargs["num_inference_steps"] = num_inference_steps
+
+            # copy over dummy past residuals (must be done after set_timesteps)
+            dummy_past_residuals = [residual + 0.2, residual + 0.15, residual + 0.10]
+            scheduler.model_outputs = dummy_past_residuals[: scheduler.config.solver_order]
+
+            time_step_0 = scheduler.timesteps[5]
+            time_step_1 = scheduler.timesteps[6]
+
+            output_0 = scheduler.step(residual, time_step_0, sample, **kwargs).prev_sample
+            output_1 = scheduler.step(residual, time_step_1, sample, **kwargs).prev_sample
+
+            self.assertEqual(output_0.shape, sample.shape)
+            self.assertEqual(output_0.shape, output_1.shape)
+
+    def test_timesteps(self):
+        for timesteps in [25, 50, 100, 999, 1000]:
+            self.check_over_configs(num_train_timesteps=timesteps)
+
+    def test_thresholding(self):
+        self.check_over_configs(thresholding=False)
+        for order in [1, 2, 3]:
+            for solver_type in ["logrho"]:
+                for threshold in [0.5, 1.0, 2.0]:
+                    for prediction_type in ["epsilon", "sample"]:
+                        self.check_over_configs(
+                            thresholding=True,
+                            prediction_type=prediction_type,
+                            sample_max_value=threshold,
+                            algorithm_type="deis",
+                            solver_order=order,
+                            solver_type=solver_type,
+                        )
+
+    def test_prediction_type(self):
+        for prediction_type in ["epsilon", "v_prediction"]:
+            self.check_over_configs(prediction_type=prediction_type)
+
+    def test_solver_order_and_type(self):
+        for algorithm_type in ["deis"]:
+            for solver_type in ["logrho"]:
+                for order in [1, 2, 3]:
+                    for prediction_type in ["epsilon", "sample"]:
+                        self.check_over_configs(
+                            solver_order=order,
+                            solver_type=solver_type,
+                            prediction_type=prediction_type,
+                            algorithm_type=algorithm_type,
+                        )
+                        sample = self.full_loop(
+                            solver_order=order,
+                            solver_type=solver_type,
+                            prediction_type=prediction_type,
+                            algorithm_type=algorithm_type,
+                        )
+                        assert not torch.isnan(sample).any(), "Samples have nan numbers"
+
+    def test_lower_order_final(self):
+        self.check_over_configs(lower_order_final=True)
+        self.check_over_configs(lower_order_final=False)
+
+    def test_inference_steps(self):
+        for num_inference_steps in [1, 2, 3, 5, 10, 50, 100, 999, 1000]:
+            self.check_over_forward(num_inference_steps=num_inference_steps, time_step=0)
+
+    def test_full_loop_no_noise(self):
+        sample = self.full_loop()
+        result_mean = torch.mean(torch.abs(sample))
+
+        assert abs(result_mean.item() - 0.23916) < 1e-3
+
+    def test_full_loop_with_v_prediction(self):
+        sample = self.full_loop(prediction_type="v_prediction")
+        result_mean = torch.mean(torch.abs(sample))
+
+        assert abs(result_mean.item() - 0.091) < 1e-3
+
+    def test_fp16_support(self):
+        scheduler_class = self.scheduler_classes[0]
+        scheduler_config = self.get_scheduler_config(thresholding=True, dynamic_thresholding_ratio=0)
+        scheduler = scheduler_class(**scheduler_config)
+
+        num_inference_steps = 10
+        model = self.dummy_model()
+        sample = self.dummy_sample_deter.half()
+        scheduler.set_timesteps(num_inference_steps)
+
+        for i, t in enumerate(scheduler.timesteps):
+            residual = model(sample, t)
+            sample = scheduler.step(residual, t, sample).prev_sample
+
+        assert sample.dtype == torch.float16
+
+
 class KDPM2AncestralDiscreteSchedulerTest(SchedulerCommonTest):
     scheduler_classes = (KDPM2AncestralDiscreteScheduler,)
     num_inference_steps = 10