scheduling_ddpm.py

# Copyright 2023 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
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# DISCLAIMER: This file is strongly influenced by https://github.com/ermongroup/ddim

import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin


@dataclass
class DDPMSchedulerOutput(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_original_sample (`torch.FloatTensor` 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_original_sample` can be used to preview progress or for guidance.
    """

    prev_sample: torch.FloatTensor
    pred_original_sample: Optional[torch.FloatTensor] = None


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)


class DDPMScheduler(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 `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.

    For more details, see the original paper: https://arxiv.org/abs/2006.11239

    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`, `squaredcos_cap_v2` or `sigmoid`.
        trained_betas (`np.ndarray`, optional):
            option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
        variance_type (`str`):
            options to clip the variance used when adding noise to the denoised sample. Choose from `fixed_small`,
            `fixed_small_log`, `fixed_large`, `fixed_large_log`, `learned` or `learned_range`.
        clip_sample (`bool`, default `True`):
            option to clip predicted sample for numerical stability.
        clip_sample_range (`float`, default `1.0`):
            the maximum magnitude for sample clipping. Valid only when `clip_sample=True`.
        prediction_type (`str`, default `epsilon`, optional):
            prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion
            process), `sample` (directly predicting the noisy sample`) or `v_prediction` (see section 2.4
            https://imagen.research.google/video/paper.pdf)
        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). Valid only when `thresholding=True`.
        sample_max_value (`float`, default `1.0`):
            the threshold value for dynamic thresholding. Valid only when `thresholding=True`.
        timestep_spacing (`str`, default `"leading"`):
            The way the timesteps should be scaled. Refer to Table 2. of [Common Diffusion Noise Schedules and Sample
            Steps are Flawed](https://arxiv.org/abs/2305.08891) for more information.
        steps_offset (`int`, default `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, as done in
            stable diffusion.
    """

    _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: Optional[Union[np.ndarray, List[float]]] = None,
        variance_type: str = "fixed_small",
        clip_sample: bool = True,
        prediction_type: str = "epsilon",
        thresholding: bool = False,
        dynamic_thresholding_ratio: float = 0.995,
        clip_sample_range: float = 1.0,
        sample_max_value: float = 1.0,
        timestep_spacing: str = "leading",
        steps_offset: int = 0,
    ):
        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)
        elif beta_schedule == "sigmoid":
            # GeoDiff sigmoid schedule
            betas = torch.linspace(-6, 6, num_train_timesteps)
            self.betas = torch.sigmoid(betas) * (beta_end - beta_start) + beta_start
        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)
        self.one = torch.tensor(1.0)

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

        # setable values
        self.custom_timesteps = False
        self.num_inference_steps = None
        self.timesteps = torch.from_numpy(np.arange(0, num_train_timesteps)[::-1].copy())

        self.variance_type = variance_type

    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`): input sample
            timestep (`int`, optional): current timestep

        Returns:
            `torch.FloatTensor`: scaled input sample
        """
        return sample

    def set_timesteps(
        self,
        num_inference_steps: Optional[int] = None,
        device: Union[str, torch.device] = None,
        timesteps: Optional[List[int]] = None,
    ):
        """
        Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.

        Args:
            num_inference_steps (`Optional[int]`):
                the number of diffusion steps used when generating samples with a pre-trained model. If passed, then
                `timesteps` must be `None`.
            device (`str` or `torch.device`, optional):
                the device to which the timesteps are moved to.
            custom_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 is used. If passed, `num_inference_steps`
                must be `None`.

        """
        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`.")

        if timesteps is not None:
            for i in range(1, len(timesteps)):
                if timesteps[i] >= timesteps[i - 1]:
                    raise ValueError("`custom_timesteps` must be in descending order.")

            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}."
                )

            timesteps = np.array(timesteps, dtype=np.int64)
            self.custom_timesteps = True
        else:
            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
            self.custom_timesteps = False

            # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/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 'linspace', 'leading' or 'trailing'."
                )

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

    def _get_variance(self, t, predicted_variance=None, variance_type=None):
        prev_t = self.previous_timestep(t)

        alpha_prod_t = self.alphas_cumprod[t]
        alpha_prod_t_prev = self.alphas_cumprod[prev_t] if prev_t >= 0 else self.one
        current_beta_t = 1 - alpha_prod_t / alpha_prod_t_prev

        # For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
        # and sample from it to get previous sample
        # x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
        variance = (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * current_beta_t

        # we always take the log of variance, so clamp it to ensure it's not 0
        variance = torch.clamp(variance, min=1e-20)

        if variance_type is None:
            variance_type = self.config.variance_type

        # hacks - were probably added for training stability
        if variance_type == "fixed_small":
            variance = variance
        # for rl-diffuser https://arxiv.org/abs/2205.09991
        elif variance_type == "fixed_small_log":
            variance = torch.log(variance)
            variance = torch.exp(0.5 * variance)
        elif variance_type == "fixed_large":
            variance = current_beta_t
        elif variance_type == "fixed_large_log":
            # Glide max_log
            variance = torch.log(current_beta_t)
        elif variance_type == "learned":
            return predicted_variance
        elif variance_type == "learned_range":
            min_log = torch.log(variance)
            max_log = torch.log(current_beta_t)
            frac = (predicted_variance + 1) / 2
            variance = frac * max_log + (1 - frac) * min_log

        return variance

    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, height, width = 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 * height * width)

        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, height, width)
        sample = sample.to(dtype)

        return sample

    def step(
        self,
        model_output: torch.FloatTensor,
        timestep: int,
        sample: torch.FloatTensor,
        generator=None,
        return_dict: bool = True,
    ) -> Union[DDPMSchedulerOutput, Tuple]:
        """
        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.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.
            generator: random number generator.
            return_dict (`bool`): option for returning tuple rather than DDPMSchedulerOutput class

        Returns:
            [`~schedulers.scheduling_utils.DDPMSchedulerOutput`] or `tuple`:
            [`~schedulers.scheduling_utils.DDPMSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When
            returning a tuple, the first element is the sample tensor.

        """
        t = timestep

        prev_t = self.previous_timestep(t)

        if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type in ["learned", "learned_range"]:
            model_output, predicted_variance = torch.split(model_output, sample.shape[1], dim=1)
        else:
            predicted_variance = None

        # 1. compute alphas, betas
        alpha_prod_t = self.alphas_cumprod[t]
        alpha_prod_t_prev = self.alphas_cumprod[prev_t] if prev_t >= 0 else self.one
        beta_prod_t = 1 - alpha_prod_t
        beta_prod_t_prev = 1 - alpha_prod_t_prev
        current_alpha_t = alpha_prod_t / alpha_prod_t_prev
        current_beta_t = 1 - current_alpha_t

        # 2. compute predicted original sample from predicted noise also called
        # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
        if self.config.prediction_type == "epsilon":
            pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)
        elif self.config.prediction_type == "sample":
            pred_original_sample = model_output
        elif self.config.prediction_type == "v_prediction":
            pred_original_sample = (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * 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 DDPMScheduler."
            )

        # 3. Clip or threshold "predicted x_0"
        if self.config.thresholding:
            pred_original_sample = self._threshold_sample(pred_original_sample)
        elif self.config.clip_sample:
            pred_original_sample = pred_original_sample.clamp(
                -self.config.clip_sample_range, self.config.clip_sample_range
            )

        # 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
        # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
        pred_original_sample_coeff = (alpha_prod_t_prev ** (0.5) * current_beta_t) / beta_prod_t
        current_sample_coeff = current_alpha_t ** (0.5) * beta_prod_t_prev / beta_prod_t

        # 5. Compute predicted previous sample µ_t
        # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
        pred_prev_sample = pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

        # 6. Add noise
        variance = 0
        if t > 0:
            device = model_output.device
            variance_noise = randn_tensor(
                model_output.shape, generator=generator, device=device, dtype=model_output.dtype
            )
            if self.variance_type == "fixed_small_log":
                variance = self._get_variance(t, predicted_variance=predicted_variance) * variance_noise
            elif self.variance_type == "learned_range":
                variance = self._get_variance(t, predicted_variance=predicted_variance)
                variance = torch.exp(0.5 * variance) * variance_noise
            else:
                variance = (self._get_variance(t, predicted_variance=predicted_variance) ** 0.5) * variance_noise

        pred_prev_sample = pred_prev_sample + variance

        if not return_dict:
            return (pred_prev_sample,)

        return DDPMSchedulerOutput(prev_sample=pred_prev_sample, pred_original_sample=pred_original_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
        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

    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

    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