Upload scheduling_tcd.py

scheduling_tcd.py

@@ -0,0 +1,657 @@
+# Copyright 2023 Stanford University Team 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: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
+# and https://github.com/hojonathanho/diffusion
+
+import math
+from dataclasses import dataclass
+from typing import List, Optional, Tuple, Union
+
+import numpy as np
+import torch
+
+from diffusers.configuration_utils import ConfigMixin, register_to_config
+from diffusers.utils import BaseOutput, logging
+from diffusers.utils.torch_utils import randn_tensor
+from diffusers.schedulers.scheduling_utils import SchedulerMixin
+
+
+logger = logging.get_logger(__name__)  # pylint: disable=invalid-name
+
+
+@dataclass
+class TCDSchedulerOutput(BaseOutput):
+    """
+    Output class for the scheduler's `step` function output.
+
+    Args:
+        prev_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
+            Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the
+            denoising loop.
+        pred_noised_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
+            The predicted noised sample `(x_{s})` based on the model output from the current timestep.
+    """
+
+    prev_sample: torch.FloatTensor
+    pred_noised_sample: Optional[torch.FloatTensor] = None
+
+
+# Copied from diffusers.schedulers.scheduling_ddpm.betas_for_alpha_bar
+def betas_for_alpha_bar(
+    num_diffusion_timesteps,
+    max_beta=0.999,
+    alpha_transform_type="cosine",
+):
+    """
+    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.
+        alpha_transform_type (`str`, *optional*, default to `cosine`): the type of noise schedule for alpha_bar.
+                     Choose from `cosine` or `exp`
+
+    Returns:
+        betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
+    """
+    if alpha_transform_type == "cosine":
+
+        def alpha_bar_fn(t):
+            return math.cos((t + 0.008) / 1.008 * math.pi / 2) ** 2
+
+    elif alpha_transform_type == "exp":
+
+        def alpha_bar_fn(t):
+            return math.exp(t * -12.0)
+
+    else:
+        raise ValueError(f"Unsupported alpha_tranform_type: {alpha_transform_type}")
+
+    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_fn(t2) / alpha_bar_fn(t1), max_beta))
+    return torch.tensor(betas, dtype=torch.float32)
+
+
+# Copied from diffusers.schedulers.scheduling_ddim.rescale_zero_terminal_snr
+def rescale_zero_terminal_snr(betas: torch.FloatTensor) -> torch.FloatTensor:
+    """
+    Rescales betas to have zero terminal SNR Based on https://arxiv.org/pdf/2305.08891.pdf (Algorithm 1)
+
+
+    Args:
+        betas (`torch.FloatTensor`):
+            the betas that the scheduler is being initialized with.
+
+    Returns:
+        `torch.FloatTensor`: rescaled betas with zero terminal SNR
+    """
+    # Convert betas to alphas_bar_sqrt
+    alphas = 1.0 - betas
+    alphas_cumprod = torch.cumprod(alphas, dim=0)
+    alphas_bar_sqrt = alphas_cumprod.sqrt()
+
+    # Store old values.
+    alphas_bar_sqrt_0 = alphas_bar_sqrt[0].clone()
+    alphas_bar_sqrt_T = alphas_bar_sqrt[-1].clone()
+
+    # Shift so the last timestep is zero.
+    alphas_bar_sqrt -= alphas_bar_sqrt_T
+
+    # Scale so the first timestep is back to the old value.
+    alphas_bar_sqrt *= alphas_bar_sqrt_0 / (alphas_bar_sqrt_0 - alphas_bar_sqrt_T)
+
+    # Convert alphas_bar_sqrt to betas
+    alphas_bar = alphas_bar_sqrt**2  # Revert sqrt
+    alphas = alphas_bar[1:] / alphas_bar[:-1]  # Revert cumprod
+    alphas = torch.cat([alphas_bar[0:1], alphas])
+    betas = 1 - alphas
+
+    return betas
+
+
+class TCDScheduler(SchedulerMixin, ConfigMixin):
+    """
+    `TCDScheduler` incorporates the `Strategic Stochastic Sampling` introduced by the paper `Trajectory Consistency Distillation`, 
+    extending the original Multistep Consistency Sampling to enable unrestricted trajectory traversal.
+
+    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. [`~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`, defaults to 1000):
+            The number of diffusion steps to train the model.
+        beta_start (`float`, defaults to 0.0001):
+            The starting `beta` value of inference.
+        beta_end (`float`, defaults to 0.02):
+            The final `beta` value.
+        beta_schedule (`str`, defaults to `"linear"`):
+            The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
+            `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
+        trained_betas (`np.ndarray`, *optional*):
+            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
+        original_inference_steps (`int`, *optional*, defaults to 50):
+            The default number of inference steps used to generate a linearly-spaced timestep schedule, from which we
+            will ultimately take `num_inference_steps` evenly spaced timesteps to form the final timestep schedule.
+        clip_sample (`bool`, defaults to `True`):
+            Clip the predicted sample for numerical stability.
+        clip_sample_range (`float`, defaults to 1.0):
+            The maximum magnitude for sample clipping. Valid only when `clip_sample=True`.
+        set_alpha_to_one (`bool`, defaults to `True`):
+            Each diffusion step uses the alphas product value at that step and at the previous one. For the final step
+            there is no previous alpha. When this option is `True` the previous alpha product is fixed to `1`,
+            otherwise it uses the alpha value at step 0.
+        steps_offset (`int`, defaults to 0):
+            An offset added to the inference steps. You can use a combination of `offset=1` and
+            `set_alpha_to_one=False` to make the last step use step 0 for the previous alpha product like in Stable
+            Diffusion.
+        prediction_type (`str`, defaults to `epsilon`, *optional*):
+            Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
+            `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen
+            Video](https://imagen.research.google/video/paper.pdf) paper).
+        thresholding (`bool`, defaults to `False`):
+            Whether to use the "dynamic thresholding" method. This is unsuitable for latent-space diffusion models such
+            as Stable Diffusion.
+        dynamic_thresholding_ratio (`float`, defaults to 0.995):
+            The ratio for the dynamic thresholding method. Valid only when `thresholding=True`.
+        sample_max_value (`float`, defaults to 1.0):
+            The threshold value for dynamic thresholding. Valid only when `thresholding=True`.
+        timestep_spacing (`str`, defaults to `"leading"`):
+            The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
+            Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
+        timestep_scaling (`float`, defaults to 10.0):
+            The factor the timesteps will be multiplied by when calculating the consistency model boundary conditions
+            `c_skip` and `c_out`. Increasing this will decrease the approximation error (although the approximation
+            error at the default of `10.0` is already pretty small).
+        rescale_betas_zero_snr (`bool`, defaults to `False`):
+            Whether to rescale the betas to have zero terminal SNR. This enables the model to generate very bright and
+            dark samples instead of limiting it to samples with medium brightness. Loosely related to
+            [`--offset_noise`](https://github.com/huggingface/diffusers/blob/74fd735eb073eb1d774b1ab4154a0876eb82f055/examples/dreambooth/train_dreambooth.py#L506).
+    """
+
+    order = 1
+
+    @register_to_config
+    def __init__(
+        self,
+        num_train_timesteps: int = 1000,
+        beta_start: float = 0.00085,
+        beta_end: float = 0.012,
+        beta_schedule: str = "scaled_linear",
+        trained_betas: Optional[Union[np.ndarray, List[float]]] = None,
+        original_inference_steps: int = 50,
+        clip_sample: bool = False,
+        clip_sample_range: float = 1.0,
+        set_alpha_to_one: bool = True,
+        steps_offset: int = 0,
+        prediction_type: str = "epsilon",
+        thresholding: bool = False,
+        dynamic_thresholding_ratio: float = 0.995,
+        sample_max_value: float = 1.0,
+        timestep_spacing: str = "leading",
+        timestep_scaling: float = 10.0,
+        rescale_betas_zero_snr: bool = False,
+    ):
+        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__}")
+
+        # Rescale for zero SNR
+        if rescale_betas_zero_snr:
+            self.betas = rescale_zero_terminal_snr(self.betas)
+
+        self.alphas = 1.0 - self.betas
+        self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
+
+        # At every step in ddim, we are looking into the previous alphas_cumprod
+        # For the final step, there is no previous alphas_cumprod because we are already at 0
+        # `set_alpha_to_one` decides whether we set this parameter simply to one or
+        # whether we use the final alpha of the "non-previous" one.
+        self.final_alpha_cumprod = torch.tensor(1.0) if set_alpha_to_one else self.alphas_cumprod[0]
+
+        # standard deviation of the initial noise distribution
+        self.init_noise_sigma = 1.0
+
+        # setable values
+        self.num_inference_steps = None
+        self.timesteps = torch.from_numpy(np.arange(0, num_train_timesteps)[::-1].copy().astype(np.int64))
+        self.custom_timesteps = False
+
+        self._step_index = None
+
+    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._init_step_index
+    def _init_step_index(self, timestep):
+        if isinstance(timestep, torch.Tensor):
+            timestep = timestep.to(self.timesteps.device)
+
+        index_candidates = (self.timesteps == timestep).nonzero()
+
+        # The sigma index that is taken for the **very** first `step`
+        # is always the second index (or the last index if there is only 1)
+        # This way we can ensure we don't accidentally skip a sigma in
+        # case we start in the middle of the denoising schedule (e.g. for image-to-image)
+        if len(index_candidates) > 1:
+            step_index = index_candidates[1]
+        else:
+            step_index = index_candidates[0]
+
+        self._step_index = step_index.item()
+
+    @property
+    def step_index(self):
+        return self._step_index
+
+    def scale_model_input(self, sample: torch.FloatTensor, timestep: Optional[int] = None) -> torch.FloatTensor:
+        """
+        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
+        current timestep.
+
+        Args:
+            sample (`torch.FloatTensor`):
+                The input sample.
+            timestep (`int`, *optional*):
+                The current timestep in the diffusion chain.
+        Returns:
+            `torch.FloatTensor`:
+                A scaled input sample.
+        """
+        return sample
+
+    def _get_variance(self, timestep, prev_timestep):
+        alpha_prod_t = self.alphas_cumprod[timestep]
+        alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
+        beta_prod_t = 1 - alpha_prod_t
+        beta_prod_t_prev = 1 - alpha_prod_t_prev
+
+        variance = (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)
+
+        return variance
+
+    # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler._threshold_sample
+    def _threshold_sample(self, sample: torch.FloatTensor) -> torch.FloatTensor:
+        """
+        "Dynamic thresholding: At each sampling step we set s to a certain percentile absolute pixel value in xt0 (the
+        prediction of x_0 at timestep t), and if s > 1, then we threshold xt0 to the range [-s, s] and then divide by
+        s. Dynamic thresholding pushes saturated pixels (those near -1 and 1) inwards, thereby actively preventing
+        pixels from saturation at each step. We find that dynamic thresholding results in significantly better
+        photorealism as well as better image-text alignment, especially when using very large guidance weights."
+
+        https://arxiv.org/abs/2205.11487
+        """
+        dtype = sample.dtype
+        batch_size, channels, *remaining_dims = sample.shape
+
+        if dtype not in (torch.float32, torch.float64):
+            sample = sample.float()  # upcast for quantile calculation, and clamp not implemented for cpu half
+
+        # Flatten sample for doing quantile calculation along each image
+        sample = sample.reshape(batch_size, channels * np.prod(remaining_dims))
+
+        abs_sample = sample.abs()  # "a certain percentile absolute pixel value"
+
+        s = torch.quantile(abs_sample, self.config.dynamic_thresholding_ratio, dim=1)
+        s = torch.clamp(
+            s, min=1, max=self.config.sample_max_value
+        )  # When clamped to min=1, equivalent to standard clipping to [-1, 1]
+        s = s.unsqueeze(1)  # (batch_size, 1) because clamp will broadcast along dim=0
+        sample = torch.clamp(sample, -s, s) / s  # "we threshold xt0 to the range [-s, s] and then divide by s"
+
+        sample = sample.reshape(batch_size, channels, *remaining_dims)
+        sample = sample.to(dtype)
+
+        return sample
+
+    def set_timesteps(
+        self,
+        num_inference_steps: Optional[int] = None,
+        device: Union[str, torch.device] = None,
+        original_inference_steps: Optional[int] = None,
+        timesteps: Optional[List[int]] = None,
+        strength: int = 1.0,
+    ):
+        """
+        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
+
+        Args:
+            num_inference_steps (`int`, *optional*):
+                The number of diffusion steps used when generating samples with a pre-trained model. If used,
+                `timesteps` must be `None`.
+            device (`str` or `torch.device`, *optional*):
+                The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
+            original_inference_steps (`int`, *optional*):
+                The original number of inference steps, which will be used to generate a linearly-spaced timestep
+                schedule (which is different from the standard `diffusers` implementation). We will then take
+                `num_inference_steps` timesteps from this schedule, evenly spaced in terms of indices, and use that as
+                our final timestep schedule. If not set, this will default to the `original_inference_steps` attribute.
+            timesteps (`List[int]`, *optional*):
+                Custom timesteps used to support arbitrary spacing between timesteps. If `None`, then the default
+                timestep spacing strategy of equal spacing between timesteps on the training/distillation timestep
+                schedule is used. If `timesteps` is passed, `num_inference_steps` must be `None`.
+        """
+        # 0. Check inputs
+        if num_inference_steps is None and timesteps is None:
+            raise ValueError("Must pass exactly one of `num_inference_steps` or `custom_timesteps`.")
+
+        if num_inference_steps is not None and timesteps is not None:
+            raise ValueError("Can only pass one of `num_inference_steps` or `custom_timesteps`.")
+
+        # 1. Calculate the TCD original training/distillation timestep schedule.
+        original_steps = (
+            original_inference_steps if original_inference_steps is not None else self.config.original_inference_steps
+        )
+        
+        if original_steps is not None:
+            if original_steps > self.config.num_train_timesteps:
+                raise ValueError(
+                    f"`original_steps`: {original_steps} cannot be larger than `self.config.train_timesteps`:"
+                    f" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle"
+                    f" maximal {self.config.num_train_timesteps} timesteps."
+                )
+            # TCD Timesteps Setting
+            # The skipping step parameter k from the paper.
+            k = self.config.num_train_timesteps // original_steps
+            # TCD Training/Distillation Steps Schedule
+            tcd_origin_timesteps = np.asarray(list(range(1, int(original_steps * strength) + 1))) * k - 1
+        else:
+            tcd_origin_timesteps = np.asarray(list(range(0, int(self.config.num_train_timesteps * strength))))
+
+        # 2. Calculate the TCD inference timestep schedule.
+        if timesteps is not None:
+            # 2.1 Handle custom timestep schedules.
+            train_timesteps = set(tcd_origin_timesteps)
+            non_train_timesteps = []
+            for i in range(1, len(timesteps)):
+                if timesteps[i] >= timesteps[i - 1]:
+                    raise ValueError("`custom_timesteps` must be in descending order.")
+
+                if timesteps[i] not in train_timesteps:
+                    non_train_timesteps.append(timesteps[i])
+
+            if timesteps[0] >= self.config.num_train_timesteps:
+                raise ValueError(
+                    f"`timesteps` must start before `self.config.train_timesteps`:"
+                    f" {self.config.num_train_timesteps}."
+                )
+
+            # Raise warning if timestep schedule does not start with self.config.num_train_timesteps - 1
+            if strength == 1.0 and timesteps[0] != self.config.num_train_timesteps - 1:
+                logger.warning(
+                    f"The first timestep on the custom timestep schedule is {timesteps[0]}, not"
+                    f" `self.config.num_train_timesteps - 1`: {self.config.num_train_timesteps - 1}. You may get"
+                    f" unexpected results when using this timestep schedule."
+                )
+
+            # Raise warning if custom timestep schedule contains timesteps not on original timestep schedule
+            if non_train_timesteps:
+                logger.warning(
+                    f"The custom timestep schedule contains the following timesteps which are not on the original"
+                    f" training/distillation timestep schedule: {non_train_timesteps}. You may get unexpected results"
+                    f" when using this timestep schedule."
+                )
+
+            # Raise warning if custom timestep schedule is longer than original_steps
+            if original_steps is not None:
+                if len(timesteps) > original_steps:
+                    logger.warning(
+                        f"The number of timesteps in the custom timestep schedule is {len(timesteps)}, which exceeds the"
+                        f" the length of the timestep schedule used for training: {original_steps}. You may get some"
+                        f" unexpected results when using this timestep schedule."
+                    )
+            else:
+                if len(timesteps) > self.config.num_train_timesteps:
+                    logger.warning(
+                        f"The number of timesteps in the custom timestep schedule is {len(timesteps)}, which exceeds the"
+                        f" the length of the timestep schedule used for training: {self.config.num_train_timesteps}. You may get some"
+                        f" unexpected results when using this timestep schedule."
+                    )
+
+            timesteps = np.array(timesteps, dtype=np.int64)
+            self.num_inference_steps = len(timesteps)
+            self.custom_timesteps = True
+
+            # Apply strength (e.g. for img2img pipelines) (see StableDiffusionImg2ImgPipeline.get_timesteps)
+            init_timestep = min(int(self.num_inference_steps * strength), self.num_inference_steps)
+            t_start = max(self.num_inference_steps - init_timestep, 0)
+            timesteps = timesteps[t_start * self.order :]
+            # TODO: also reset self.num_inference_steps?
+        else:
+            # 2.2 Create the "standard" TCD inference timestep schedule.
+            if num_inference_steps > self.config.num_train_timesteps:
+                raise ValueError(
+                    f"`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:"
+                    f" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle"
+                    f" maximal {self.config.num_train_timesteps} timesteps."
+                )
+
+            if original_steps is not None:
+                skipping_step = len(tcd_origin_timesteps) // num_inference_steps
+
+                if skipping_step < 1:
+                    raise ValueError(
+                        f"The combination of `original_steps x strength`: {original_steps} x {strength} is smaller than `num_inference_steps`: {num_inference_steps}. Make sure to either reduce `num_inference_steps` to a value smaller than {int(original_steps * strength)} or increase `strength` to a value higher than {float(num_inference_steps / original_steps)}."
+                    )
+
+            self.num_inference_steps = num_inference_steps
+
+            if original_steps is not None:
+                if num_inference_steps > original_steps:
+                    raise ValueError(
+                        f"`num_inference_steps`: {num_inference_steps} cannot be larger than `original_inference_steps`:"
+                        f" {original_steps} because the final timestep schedule will be a subset of the"
+                        f" `original_inference_steps`-sized initial timestep schedule."
+                    )
+            else:
+                if num_inference_steps > self.config.num_train_timesteps:
+                    raise ValueError(
+                        f"`num_inference_steps`: {num_inference_steps} cannot be larger than `num_train_timesteps`:"
+                        f" {self.config.num_train_timesteps} because the final timestep schedule will be a subset of the"
+                        f" `num_train_timesteps`-sized initial timestep schedule."
+                    )
+
+            # TCD Inference Steps Schedule
+            tcd_origin_timesteps = tcd_origin_timesteps[::-1].copy()
+            # Select (approximately) evenly spaced indices from tcd_origin_timesteps.
+            inference_indices = np.linspace(0, len(tcd_origin_timesteps), num=num_inference_steps, endpoint=False)
+            inference_indices = np.floor(inference_indices).astype(np.int64)
+            timesteps = tcd_origin_timesteps[inference_indices]
+
+        self.timesteps = torch.from_numpy(timesteps).to(device=device, dtype=torch.long)
+
+        self._step_index = None
+
+    def step(
+        self,
+        model_output: torch.FloatTensor,
+        timestep: int,
+        sample: torch.FloatTensor,
+        eta: float,
+        generator: Optional[torch.Generator] = None,
+        return_dict: bool = True,
+    ) -> Union[TCDSchedulerOutput, Tuple]:
+        """
+        Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
+        process from the learned model outputs (most often the predicted noise).
+
+        Args:
+            model_output (`torch.FloatTensor`):
+                The direct output from learned diffusion model.
+            timestep (`int`):
+                The current discrete timestep in the diffusion chain.
+            sample (`torch.FloatTensor`):
+                A current instance of a sample created by the diffusion process.
+            eta (`float`):
+                A stochastic parameter (referred to as `gamma` in the paper) used to control the stochasticity in every step. 
+                When eta = 0, it represents deterministic sampling, whereas eta = 1 indicates full stochastic sampling.
+            generator (`torch.Generator`, *optional*):
+                A random number generator.
+            return_dict (`bool`, *optional*, defaults to `True`):
+                Whether or not to return a [`~schedulers.scheduling_tcd.TCDSchedulerOutput`] or `tuple`.
+        Returns:
+            [`~schedulers.scheduling_utils.TCDSchedulerOutput`] or `tuple`:
+                If return_dict is `True`, [`~schedulers.scheduling_tcd.TCDSchedulerOutput`] is returned, otherwise a
+                tuple is returned where 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 self.step_index is None:
+            self._init_step_index(timestep)
+
+        # 1. get previous step value
+        prev_step_index = self.step_index + 1
+        if prev_step_index < len(self.timesteps):
+            prev_timestep = self.timesteps[prev_step_index]
+        else:
+            prev_timestep = torch.tensor(0)
+
+        timestep_s = torch.floor((1 - eta) * prev_timestep).to(dtype=torch.long)
+        
+        # 2. compute alphas, betas
+        alpha_prod_t = self.alphas_cumprod[timestep]
+        beta_prod_t = 1 - alpha_prod_t
+
+        alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
+        beta_prod_t_prev = 1 - alpha_prod_t_prev
+        
+        alpha_prod_s = self.alphas_cumprod[timestep_s] if timestep_s >= 0 else self.final_alpha_cumprod
+        beta_prod_s = 1 - alpha_prod_s
+
+        # 3. Compute the predicted noised sample x_s based on the model parameterization
+        if self.config.prediction_type == "epsilon":  # noise-prediction
+            pred_original_sample = (sample - beta_prod_t.sqrt() * model_output) / alpha_prod_t.sqrt()
+            pred_epsilon = model_output
+            pred_noised_sample = alpha_prod_s.sqrt() * pred_original_sample + beta_prod_s.sqrt() * pred_epsilon 
+        elif self.config.prediction_type == "sample":  # x-prediction
+            pred_original_sample = model_output
+            pred_epsilon = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5)
+            pred_noised_sample = alpha_prod_s.sqrt() * pred_original_sample + beta_prod_s.sqrt() * pred_epsilon
+        elif self.config.prediction_type == "v_prediction":  # v-prediction
+            pred_original_sample = (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
+            pred_epsilon = (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
+            pred_noised_sample = alpha_prod_s.sqrt() * pred_original_sample + beta_prod_s.sqrt() * pred_epsilon
+        else:
+            raise ValueError(
+                f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` or"
+                " `v_prediction` for `TCDScheduler`."
+            )
+            
+        # 4. Sample and inject noise z ~ N(0, I) for MultiStep Inference
+        # Noise is not used on the final timestep of the timestep schedule.
+        # This also means that noise is not used for one-step sampling.
+        # Eta (referred to as "gamma" in the paper) was introduced to control the stochasticity in every step. 
+        # When eta = 0, it represents deterministic sampling, whereas eta = 1 indicates full stochastic sampling.
+        if eta > 0:
+            if self.step_index != self.num_inference_steps - 1:
+                noise = randn_tensor(
+                    model_output.shape, generator=generator, device=model_output.device, dtype=pred_noised_sample.dtype
+                )
+                prev_sample = (alpha_prod_t_prev / alpha_prod_s).sqrt() * pred_noised_sample + (1 - alpha_prod_t_prev / alpha_prod_s).sqrt() * noise
+            else:
+                prev_sample = pred_noised_sample
+        else:
+            prev_sample = pred_noised_sample
+
+        # upon completion increase step index by one
+        self._step_index += 1
+
+        if not return_dict:
+            return (prev_sample, pred_noised_sample)
+
+        return TCDSchedulerOutput(prev_sample=prev_sample, pred_noised_sample=pred_noised_sample)
+
+    # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.add_noise
+    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
+        alphas_cumprod = self.alphas_cumprod.to(device=original_samples.device, dtype=original_samples.dtype)
+        timesteps = timesteps.to(original_samples.device)
+
+        sqrt_alpha_prod = 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 - 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
+
+    # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.get_velocity
+    def get_velocity(
+        self, sample: torch.FloatTensor, noise: torch.FloatTensor, timesteps: torch.IntTensor
+    ) -> torch.FloatTensor:
+        # Make sure alphas_cumprod and timestep have same device and dtype as sample
+        alphas_cumprod = self.alphas_cumprod.to(device=sample.device, dtype=sample.dtype)
+        timesteps = timesteps.to(sample.device)
+
+        sqrt_alpha_prod = alphas_cumprod[timesteps] ** 0.5
+        sqrt_alpha_prod = sqrt_alpha_prod.flatten()
+        while len(sqrt_alpha_prod.shape) < len(sample.shape):
+            sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)
+
+        sqrt_one_minus_alpha_prod = (1 - 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(sample.shape):
+            sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)
+
+        velocity = sqrt_alpha_prod * noise - sqrt_one_minus_alpha_prod * sample
+        return velocity
+
+    def __len__(self):
+        return self.config.num_train_timesteps
+
+    # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.previous_timestep
+    def previous_timestep(self, timestep):
+        if self.custom_timesteps:
+            index = (self.timesteps == timestep).nonzero(as_tuple=True)[0][0]
+            if index == self.timesteps.shape[0] - 1:
+                prev_t = torch.tensor(-1)
+            else:
+                prev_t = self.timesteps[index + 1]
+        else:
+            num_inference_steps = (
+                self.num_inference_steps if self.num_inference_steps else self.config.num_train_timesteps
+            )
+            prev_t = timestep - self.config.num_train_timesteps // num_inference_steps
+
+        return prev_t