diffusers/schedulers/scheduling_ddpm_wuerstchen.py

# Copyright (c) 2022 Pablo Pernías MIT License
# Copyright 2025 UC Berkeley 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 file is strongly influenced by https://github.com/ermongroup/ddim

import math
from dataclasses import dataclass
from typing import Literal

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 SchedulerMixin


@dataclass
class DDPMWuerstchenSchedulerOutput(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 the previous timestep. `prev_sample` should be used as the next model input
            in the denoising loop.
    """

    prev_sample: torch.Tensor


def betas_for_alpha_bar(
    num_diffusion_timesteps: int,
    max_beta: float = 0.999,
    alpha_transform_type: Literal["cosine", "exp"] = "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 prevent singularities.
        alpha_transform_type (`str`, defaults to `"cosine"`):
            The type of noise schedule for `alpha_bar`. Choose from `cosine` or `exp`.

    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 == "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)


class DDPMWuerstchenScheduler(SchedulerMixin, ConfigMixin):
    """
    Denoising diffusion probabilistic models (DDPMs) explores the connections between denoising score matching and
    Langevin dynamics sampling.

    [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
    function, such as `scaler`. They can be accessed via `scheduler.config.scaler`. [`SchedulerMixin`] provides general
    loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and [`~SchedulerMixin.from_pretrained`]
    functions.

    For more details, see the original paper: https://huggingface.co/papers/2006.11239

    Args:
        scaler (`float`, defaults to `1.0`):
            The scaling factor applied to the timesteps before computing the cumulative product of alphas.
        s (`float`, defaults to `0.008`):
            The offset added to the cosine noise schedule.
    """

    @register_to_config
    def __init__(
        self,
        scaler: float = 1.0,
        s: float = 0.008,
    ) -> None:
        self.scaler = scaler
        self.s = torch.tensor([s])
        self._init_alpha_cumprod = torch.cos(self.s / (1 + self.s) * torch.pi * 0.5) ** 2

        # standard deviation of the initial noise distribution
        self.init_noise_sigma = 1.0

    def _alpha_cumprod(self, t: torch.Tensor, device: torch.device) -> torch.Tensor:
        if self.scaler > 1:
            t = 1 - (1 - t) ** self.scaler
        elif self.scaler < 1:
            t = t**self.scaler
        alpha_cumprod = torch.cos(
            (t + self.s.to(device)) / (1 + self.s.to(device)) * torch.pi * 0.5
        ) ** 2 / self._init_alpha_cumprod.to(device)
        return alpha_cumprod.clamp(0.0001, 0.9999)

    def scale_model_input(self, sample: torch.Tensor, timestep: torch.Tensor | None = 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 (`torch.Tensor`, *optional*):
                The current timestep in the diffusion chain.

        Returns:
            `torch.Tensor`:
                A scaled input sample.
        """
        return sample

    def set_timesteps(
        self,
        num_inference_steps: int | None = None,
        timesteps: list[float] | torch.Tensor | None = None,
        device: str | torch.device | None = None,
    ) -> None:
        """
        Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.

        Args:
            num_inference_steps (`int`, *optional*):
                The number of diffusion steps used when generating samples with a pretrained model. If passed,
                `timesteps` must be `None`.
            timesteps (`list[float]` or `torch.Tensor`, *optional*):
                Custom timesteps used for the diffusion chain. If passed, `num_inference_steps` must be `None`.
            device (`str` or `torch.device`, *optional*):
                The device to which the timesteps are moved.
        """
        if timesteps is None:
            timesteps = torch.linspace(1.0, 0.0, num_inference_steps + 1, device=device)
        if not isinstance(timesteps, torch.Tensor):
            timesteps = torch.Tensor(timesteps).to(device)
        self.timesteps = timesteps

    def step(
        self,
        model_output: torch.Tensor,
        timestep: torch.Tensor,
        sample: torch.Tensor,
        generator: torch.Generator | list[torch.Generator] | None = None,
        return_dict: bool = True,
    ) -> DDPMWuerstchenSchedulerOutput | tuple[torch.Tensor]:
        """
        Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
        process from the learned model outputs (most often the predicted noise).

        Args:
            model_output (`torch.Tensor`):
                The direct output from the learned diffusion model.
            timestep (`torch.Tensor`):
                The current discrete timestep in the diffusion chain.
            sample (`torch.Tensor`):
                A current instance of a sample created by the diffusion process.
            generator (`torch.Generator` or `list[torch.Generator]`, *optional*):
                A random number generator or a list of generators to make generation deterministic.
            return_dict (`bool`, defaults to `True`):
                Whether to return a [`~schedulers.scheduling_ddpm_wuerstchen.DDPMWuerstchenSchedulerOutput`] or a
                `tuple`.

        Returns:
            [`~schedulers.scheduling_ddpm_wuerstchen.DDPMWuerstchenSchedulerOutput`] or `tuple`:
                If `return_dict` is `True`, a [`~schedulers.scheduling_ddpm_wuerstchen.DDPMWuerstchenSchedulerOutput`]
                is returned, otherwise a `tuple` is returned where the first element is the sample tensor.
        """
        dtype = model_output.dtype
        device = model_output.device
        t = timestep

        prev_t = self.previous_timestep(t)

        alpha_cumprod = self._alpha_cumprod(t, device).view(t.size(0), *[1 for _ in sample.shape[1:]])
        alpha_cumprod_prev = self._alpha_cumprod(prev_t, device).view(prev_t.size(0), *[1 for _ in sample.shape[1:]])
        alpha = alpha_cumprod / alpha_cumprod_prev

        mu = (1.0 / alpha).sqrt() * (sample - (1 - alpha) * model_output / (1 - alpha_cumprod).sqrt())

        std_noise = randn_tensor(mu.shape, generator=generator, device=model_output.device, dtype=model_output.dtype)
        std = ((1 - alpha) * (1.0 - alpha_cumprod_prev) / (1.0 - alpha_cumprod)).sqrt() * std_noise
        pred = mu + std * (prev_t != 0).float().view(prev_t.size(0), *[1 for _ in sample.shape[1:]])

        if not return_dict:
            return (pred.to(dtype),)

        return DDPMWuerstchenSchedulerOutput(prev_sample=pred.to(dtype))

    def add_noise(
        self,
        original_samples: torch.Tensor,
        noise: torch.Tensor,
        timesteps: torch.Tensor,
    ) -> torch.Tensor:
        """
        Add noise to the original samples according to the noise magnitude at each timestep.

        Args:
            original_samples (`torch.Tensor`):
                The original samples to which noise is added.
            noise (`torch.Tensor`):
                The noise to add to the original samples.
            timesteps (`torch.Tensor`):
                The timesteps that determine the noise magnitude.

        Returns:
            `torch.Tensor`:
                The noisy samples.
        """
        device = original_samples.device
        dtype = original_samples.dtype
        alpha_cumprod = self._alpha_cumprod(timesteps, device=device).view(
            timesteps.size(0), *[1 for _ in original_samples.shape[1:]]
        )
        noisy_samples = alpha_cumprod.sqrt() * original_samples + (1 - alpha_cumprod).sqrt() * noise
        return noisy_samples.to(dtype=dtype)

    def __len__(self) -> int:
        return self.config.num_train_timesteps

    def previous_timestep(self, timestep: torch.Tensor) -> torch.Tensor:
        """
        Compute the previous timestep in the diffusion chain.

        Args:
            timestep (`torch.Tensor`):
                The current timestep.

        Returns:
            `torch.Tensor`:
                The previous timestep.
        """
        index = (self.timesteps - timestep[0]).abs().argmin().item()
        prev_t = self.timesteps[index + 1][None].expand(timestep.shape[0])
        return prev_t