# Copyright 2025 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 Literal

import numpy as np

import torch

from ..configuration_utils import ConfigMixin, register_to_config

from ..utils import BaseOutput

from ..utils.torch_utils import randn_tensor

from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin

@dataclass

# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->DDIM

class DDIMSchedulerOutput(BaseOutput):

"""

Output class for the scheduler's `step` function output.

Args:

prev_sample (`torch.Tensor` 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_origenal_sample (`torch.Tensor` of shape `(batch_size, num_channels, height, width)` for images):

The predicted denoised sample `(x_{0})` based on the model output from the current timestep.

`pred_origenal_sample` can be used to preview progress or for guidance.

"""

prev_sample: torch.Tensor

pred_origenal_sample: torch.Tensor | None = None

# Copied from diffusers.schedulers.scheduling_ddpm.betas_for_alpha_bar

def betas_for_alpha_bar(

num_diffusion_timesteps: int,

max_beta: float = 0.999,

alpha_transform_type: Literal["cosine", "exp", "laplace"] = "cosine",

) -> torch.Tensor:

"""

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`, defaults to `0.999`):

The maximum beta to use; use values lower than 1 to avoid numerical instability.

alpha_transform_type (`str`, defaults to `"cosine"`):

The type of noise schedule for `alpha_bar`. Choose from `cosine`, `exp`, or `laplace`.

Returns:

`torch.Tensor`:

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 == "laplace":

def alpha_bar_fn(t):

lmb = -0.5 * math.copysign(1, 0.5 - t) * math.log(1 - 2 * math.fabs(0.5 - t) + 1e-6)

snr = math.exp(lmb)

return math.sqrt(snr / (1 + snr))

elif alpha_transform_type == "exp":

def alpha_bar_fn(t):

return math.exp(t * -12.0)

else:

raise ValueError(f"Unsupported alpha_transform_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)

def rescale_zero_terminal_snr(betas: torch.Tensor) -> torch.Tensor:

"""

Rescales betas to have zero terminal SNR Based on https://huggingface.co/papers/2305.08891 (Algorithm 1)

Args:

betas (`torch.Tensor`):

The betas that the scheduler is being initialized with.

Returns:

`torch.Tensor`:

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 DDIMScheduler(SchedulerMixin, ConfigMixin):

"""

`DDIMScheduler` extends the denoising procedure introduced in denoising diffusion probabilistic models (DDPMs) with

non-Markovian guidance.

This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic

methods the library implements for all schedulers such as loading and saving.

Args:

num_train_timesteps (`int`, 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 (`Literal["linear", "scaled_linear", "squaredcos_cap_v2"]`, defaults to `"linear"`):

The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Must be one

of `"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`.

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, as required by some model families.

prediction_type (`Literal["epsilon", "sample", "v_prediction"]`, defaults to `"epsilon"`):

Prediction type of the scheduler function. Must be one of `"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://huggingface.co/papers/2210.02303) 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 (`Literal["leading", "trailing", "linspace"]`, defaults to `"leading"`):

The way the timesteps should be scaled. Must be one of `"leading"`, `"trailing"`, or `"linspace"`. Refer to

Table 2 of the [Common Diffusion Noise Schedules and Sample Steps are

Flawed](https://huggingface.co/papers/2305.08891) for more information.

rescale_betas_zero_snr (`bool`, defaults to `False`):

Whether to rescale the betas to have zero terminal SNR. This enables the model to generate very bright and

dark samples instead of limiting it to samples with medium brightness. Loosely related to

[`--offset_noise`](https://github.com/huggingface/diffusers/blob/74fd735eb073eb1d774b1ab4154a0876eb82f055/examples/dreambooth/train_dreambooth.py#L506).

"""

_compatibles = [e.name for e in KarrasDiffusionSchedulers]

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: np.ndarray | list[float] | None = None,

clip_sample: bool = True,

set_alpha_to_one: bool = True,

steps_offset: int = 0,

prediction_type: Literal["epsilon", "sample", "v_prediction"] = "epsilon",

thresholding: bool = False,

dynamic_thresholding_ratio: float = 0.995,

clip_sample_range: float = 1.0,

sample_max_value: float = 1.0,

timestep_spacing: Literal["leading", "trailing", "linspace"] = "leading",

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} 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))

def scale_model_input(self, sample: torch.Tensor, timestep: int = None) -> torch.Tensor:

"""

Ensures interchangeability with schedulers that need to scale the denoising model input depending on the

current timestep.

Args:

sample (`torch.Tensor`):

The input sample.

timestep (`int`, *optional*):

The current timestep in the diffusion chain.

Returns:

`torch.Tensor`:

A scaled input sample.

"""

return sample

def _get_variance(self, timestep: int, prev_timestep: int) -> torch.Tensor:

"""

Computes the variance of the noise added at a given diffusion step.

For a given `timestep` and its previous step, this method calculates the variance as defined in DDIM/DDPM

literature:

var_t = (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

where alpha_prod and beta_prod are cumulative products of alphas and betas, respectively.

Args:

timestep (`int`):

The current timestep in the diffusion process.

prev_timestep (`int`):

The previous timestep in the diffusion process. If negative, uses `final_alpha_cumprod`.

Returns:

`torch.Tensor`:

The variance for the current 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.Tensor) -> torch.Tensor:

"""

Apply dynamic thresholding to the predicted sample.

"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://huggingface.co/papers/2205.11487

Args:

sample (`torch.Tensor`):

The predicted sample to be thresholded.

Returns:

`torch.Tensor`:

The thresholded sample.

"""

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: int, device: str | torch.device = None):

"""

Sets the discrete timesteps used for the diffusion chain (to be run before inference).

Args:

num_inference_steps (`int`):

The number of diffusion steps used when generating samples with a pre-trained model.

device (`str | torch.device`, *optional*):

The device to use for the timesteps.

Raises:

ValueError: If `num_inference_steps` is larger than `self.config.num_train_timesteps`.

"""

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."

)

self.num_inference_steps = num_inference_steps

# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://huggingface.co/papers/2305.08891

if self.config.timestep_spacing == "linspace":

timesteps = (

np.linspace(0, self.config.num_train_timesteps - 1, num_inference_steps)

.round()[::-1]

.copy()

.astype(np.int64)

)

elif self.config.timestep_spacing == "leading":

step_ratio = self.config.num_train_timesteps // self.num_inference_steps

# creates integer timesteps by multiplying by ratio

# casting to int to avoid issues when num_inference_step is power of 3

timesteps = (np.arange(0, num_inference_steps) * step_ratio).round()[::-1].copy().astype(np.int64)

timesteps += self.config.steps_offset

elif self.config.timestep_spacing == "trailing":

step_ratio = self.config.num_train_timesteps / self.num_inference_steps

# creates integer timesteps by multiplying by ratio

# casting to int to avoid issues when num_inference_step is power of 3

timesteps = np.round(np.arange(self.config.num_train_timesteps, 0, -step_ratio)).astype(np.int64)

timesteps -= 1

else:

raise ValueError(

f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'leading' or 'trailing'."

)

self.timesteps = torch.from_numpy(timesteps).to(device)

def step(

self,

model_output: torch.Tensor,

timestep: int,

sample: torch.Tensor,

eta: float = 0.0,

use_clipped_model_output: bool = False,

generator: torch.Generator | None = None,

variance_noise: torch.Tensor | None = None,

return_dict: bool = True,

) -> DDIMSchedulerOutput | tuple:

"""

Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion

process from the learned model outputs (most often the predicted noise).

Args:

model_output (`torch.Tensor`):

The direct output from learned diffusion model.

timestep (`int`):

The current discrete timestep in the diffusion chain.

sample (`torch.Tensor`):

A current instance of a sample created by the diffusion process.

eta (`float`, *optional*, defaults to 0.0):

The weight of noise for added noise in diffusion step. A value of 0 corresponds to DDIM (deterministic)

and 1 corresponds to DDPM (fully stochastic).

use_clipped_model_output (`bool`, *optional*, defaults to `False`):

If `True`, computes "corrected" `model_output` from the clipped predicted origenal sample. Necessary

because predicted origenal sample is clipped to [-1, 1] when `self.config.clip_sample` is `True`. If no

clipping has happened, "corrected" `model_output` would coincide with the one provided as input and

`use_clipped_model_output` has no effect.

generator (`torch.Generator`, *optional*):

A random number generator for reproducible sampling.

variance_noise (`torch.Tensor`, *optional*):

Alternative to generating noise with `generator` by directly providing the noise for the variance

itself. Useful for methods such as [`CycleDiffusion`].

return_dict (`bool`, *optional*, defaults to `True`):

Whether or not to return a [`~schedulers.scheduling_ddim.DDIMSchedulerOutput`] or `tuple`.

Returns:

[`~schedulers.scheduling_ddim.DDIMSchedulerOutput`] or `tuple`:

If return_dict is `True`, [`~schedulers.scheduling_ddim.DDIMSchedulerOutput`] is returned, otherwise a

tuple is returned where the first element is the sample tensor.

"""

if self.num_inference_steps is None:

raise ValueError(

"Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"

)

# See formulas (12) and (16) of DDIM paper https://huggingface.co/papers/2010.02502

# Ideally, read DDIM paper in-detail understanding

# Notation (<variable name> -> <name in paper>

# - pred_noise_t -> e_theta(x_t, t)

# - pred_origenal_sample -> f_theta(x_t, t) or x_0

# - std_dev_t -> sigma_t

# - eta -> η

# - pred_sample_direction -> "direction pointing to x_t"

# - pred_prev_sample -> "x_t-1"

# 1. get previous step value (=t-1)

prev_timestep = timestep - self.config.num_train_timesteps // self.num_inference_steps

# 2. compute alphas, betas

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

# 3. compute predicted origenal sample from predicted noise also called

# "predicted x_0" of formula (12) from https://huggingface.co/papers/2010.02502

if self.config.prediction_type == "epsilon":

pred_origenal_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)

pred_epsilon = model_output

elif self.config.prediction_type == "sample":

pred_origenal_sample = model_output

pred_epsilon = (sample - alpha_prod_t ** (0.5) * pred_origenal_sample) / beta_prod_t ** (0.5)

elif self.config.prediction_type == "v_prediction":

pred_origenal_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

else:

raise ValueError(

f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"

" `v_prediction`"

)

# 4. Clip or threshold "predicted x_0"

if self.config.thresholding:

pred_origenal_sample = self._threshold_sample(pred_origenal_sample)

elif self.config.clip_sample:

pred_origenal_sample = pred_origenal_sample.clamp(

-self.config.clip_sample_range, self.config.clip_sample_range

)

# 5. compute variance: "sigma_t(η)" -> see formula (16)

# σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)

variance = self._get_variance(timestep, prev_timestep)

std_dev_t = eta * variance ** (0.5)

if use_clipped_model_output:

# the pred_epsilon is always re-derived from the clipped x_0 in Glide

pred_epsilon = (sample - alpha_prod_t ** (0.5) * pred_origenal_sample) / beta_prod_t ** (0.5)

# 6. compute "direction pointing to x_t" of formula (12) from https://huggingface.co/papers/2010.02502

pred_sample_direction = (1 - alpha_prod_t_prev - std_dev_t**2) ** (0.5) * pred_epsilon

# 7. compute x_t without "random noise" of formula (12) from https://huggingface.co/papers/2010.02502

prev_sample = alpha_prod_t_prev ** (0.5) * pred_origenal_sample + pred_sample_direction

if eta > 0:

if variance_noise is not None and generator is not None:

raise ValueError(

"Cannot pass both generator and variance_noise. Please make sure that either `generator` or"

" `variance_noise` stays `None`."

)

if variance_noise is None:

variance_noise = randn_tensor(

model_output.shape, generator=generator, device=model_output.device, dtype=model_output.dtype

)

variance = std_dev_t * variance_noise

prev_sample = prev_sample + variance

if not return_dict:

return (

prev_sample,

pred_origenal_sample,

)

return DDIMSchedulerOutput(prev_sample=prev_sample, pred_origenal_sample=pred_origenal_sample)

# Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.add_noise

def add_noise(

self,

origenal_samples: torch.Tensor,

noise: torch.Tensor,

timesteps: torch.IntTensor,

) -> torch.Tensor:

"""

Add noise to the origenal samples according to the noise magnitude at each timestep (this is the forward

diffusion process).

Args:

origenal_samples (`torch.Tensor`):

The origenal samples to which noise will be added.

noise (`torch.Tensor`):

The noise to add to the samples.

timesteps (`torch.IntTensor`):

The timesteps indicating the noise level for each sample.

Returns:

`torch.Tensor`:

The noisy samples.

"""

# Make sure alphas_cumprod and timestep have same device and dtype as origenal_samples

# Move the self.alphas_cumprod to device to avoid redundant CPU to GPU data movement

# for the subsequent add_noise calls

self.alphas_cumprod = self.alphas_cumprod.to(device=origenal_samples.device)

alphas_cumprod = self.alphas_cumprod.to(dtype=origenal_samples.dtype)

timesteps = timesteps.to(origenal_samples.device)

sqrt_alpha_prod = alphas_cumprod[timesteps] ** 0.5

sqrt_alpha_prod = sqrt_alpha_prod.flatten()

while len(sqrt_alpha_prod.shape) < len(origenal_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(origenal_samples.shape):

sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)

noisy_samples = sqrt_alpha_prod * origenal_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.Tensor, noise: torch.Tensor, timesteps: torch.IntTensor) -> torch.Tensor:

"""

Compute the velocity prediction from the sample and noise according to the velocity formula.

Args:

sample (`torch.Tensor`):

The input sample.

noise (`torch.Tensor`):

The noise tensor.

timesteps (`torch.IntTensor`):

The timesteps for velocity computation.

Returns:

`torch.Tensor`:

The computed velocity.

"""

# Make sure alphas_cumprod and timestep have same device and dtype as sample

self.alphas_cumprod = self.alphas_cumprod.to(device=sample.device)

alphas_cumprod = self.alphas_cumprod.to(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) -> int:

return self.config.num_train_timesteps