scheduling_heun_discrete.py

# Copyright 2023 Katherine Crowson, The HuggingFace Team and hlky. 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.

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

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput


# Copied from diffusers.schedulers.scheduling_ddpm.betas_for_alpha_bar
def betas_for_alpha_bar(num_diffusion_timesteps, max_beta=0.999) -> 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`): the maximum beta to use; use values lower than 1 to
                     prevent singularities.

    Returns:
        betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
    """

    def alpha_bar(time_step):
        return math.cos((time_step + 0.008) / 1.008 * math.pi / 2) ** 2

    betas = []
    for i in range(num_diffusion_timesteps):
        t1 = i / num_diffusion_timesteps
        t2 = (i + 1) / num_diffusion_timesteps
        betas.append(min(1 - alpha_bar(t2) / alpha_bar(t1), max_beta))
    return torch.tensor(betas, dtype=torch.float32)


class HeunDiscreteScheduler(SchedulerMixin, ConfigMixin):
    """
    Implements Algorithm 2 (Heun steps) from Karras et al. (2022). for discrete beta schedules. Based on the original
    k-diffusion implementation by Katherine Crowson:
    https://github.com/crowsonkb/k-diffusion/blob/481677d114f6ea445aa009cf5bd7a9cdee909e47/k_diffusion/sampling.py#L90

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

    Args:
        num_train_timesteps (`int`): number of diffusion steps used to train the model. beta_start (`float`): the
        starting `beta` value of inference. beta_end (`float`): the final `beta` value. beta_schedule (`str`):
            the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
            `linear` or `scaled_linear`.
        trained_betas (`np.ndarray`, optional):
            option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
            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`.
        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)
    """

    _compatibles = [e.name for e in KarrasDiffusionSchedulers]
    order = 2

    @register_to_config
    def __init__(
        self,
        num_train_timesteps: int = 1000,
        beta_start: float = 0.00085,  # sensible defaults
        beta_end: float = 0.012,
        beta_schedule: str = "linear",
        trained_betas: Optional[Union[np.ndarray, List[float]]] = None,
        prediction_type: str = "epsilon",
    ):
        if trained_betas is not None:
            self.betas = torch.tensor(trained_betas, dtype=torch.float32)
        elif beta_schedule == "linear":
            self.betas = torch.linspace(beta_start, beta_end, num_train_timesteps, dtype=torch.float32)
        elif beta_schedule == "scaled_linear":
            # this schedule is very specific to the latent diffusion model.
            self.betas = (
                torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2
            )
        elif beta_schedule == "squaredcos_cap_v2":
            # Glide cosine schedule
            self.betas = betas_for_alpha_bar(num_train_timesteps)
        else:
            raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}")

        self.alphas = 1.0 - self.betas
        self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)

        #  set all values
        self.set_timesteps(num_train_timesteps, None, num_train_timesteps)

    def index_for_timestep(self, timestep):
        indices = (self.timesteps == timestep).nonzero()
        if self.state_in_first_order:
            pos = -1
        else:
            pos = 0
        return indices[pos].item()

    def scale_model_input(
        self,
        sample: torch.FloatTensor,
        timestep: Union[float, torch.FloatTensor],
    ) -> torch.FloatTensor:
        """
        Args:
        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
        current timestep.
            sample (`torch.FloatTensor`): input sample timestep (`int`, optional): current timestep
        Returns:
            `torch.FloatTensor`: scaled input sample
        """
        step_index = self.index_for_timestep(timestep)

        sigma = self.sigmas[step_index]
        sample = sample / ((sigma**2 + 1) ** 0.5)
        return sample

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

        Args:
            num_inference_steps (`int`):
                the number of diffusion steps used when generating samples with a pre-trained model.
            device (`str` or `torch.device`, optional):
                the device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
        """
        self.num_inference_steps = num_inference_steps

        num_train_timesteps = num_train_timesteps or self.config.num_train_timesteps

        timesteps = np.linspace(0, num_train_timesteps - 1, num_inference_steps, dtype=float)[::-1].copy()

        sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
        sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
        sigmas = np.concatenate([sigmas, [0.0]]).astype(np.float32)
        sigmas = torch.from_numpy(sigmas).to(device=device)
        self.sigmas = torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2), sigmas[-1:]])

        # standard deviation of the initial noise distribution
        self.init_noise_sigma = self.sigmas.max()

        timesteps = torch.from_numpy(timesteps)
        timesteps = torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2)])

        if str(device).startswith("mps"):
            # mps does not support float64
            self.timesteps = timesteps.to(device, dtype=torch.float32)
        else:
            self.timesteps = timesteps.to(device=device)

        # empty dt and derivative
        self.prev_derivative = None
        self.dt = None

    @property
    def state_in_first_order(self):
        return self.dt is None

    def step(
        self,
        model_output: Union[torch.FloatTensor, np.ndarray],
        timestep: Union[float, torch.FloatTensor],
        sample: Union[torch.FloatTensor, np.ndarray],
        return_dict: bool = True,
    ) -> Union[SchedulerOutput, Tuple]:
        """
        Args:
        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).
            model_output (`torch.FloatTensor` or `np.ndarray`): direct output from learned diffusion model. timestep
            (`int`): current discrete timestep in the diffusion chain. sample (`torch.FloatTensor` or `np.ndarray`):
                current instance of sample being created by diffusion process.
            return_dict (`bool`): option for returning tuple rather than SchedulerOutput class
        Returns:
            [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
            [`~schedulers.scheduling_utils.SchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When
            returning a tuple, the first element is the sample tensor.
        """
        step_index = self.index_for_timestep(timestep)

        if self.state_in_first_order:
            sigma = self.sigmas[step_index]
            sigma_next = self.sigmas[step_index + 1]
        else:
            # 2nd order / Heun's method
            sigma = self.sigmas[step_index - 1]
            sigma_next = self.sigmas[step_index]

        # currently only gamma=0 is supported. This usually works best anyways.
        # We can support gamma in the future but then need to scale the timestep before
        # passing it to the model which requires a change in API
        gamma = 0
        sigma_hat = sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

        # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
        if self.config.prediction_type == "epsilon":
            sigma_input = sigma_hat if self.state_in_first_order else sigma_next
            pred_original_sample = sample - sigma_input * model_output
        elif self.config.prediction_type == "v_prediction":
            sigma_input = sigma_hat if self.state_in_first_order else sigma_next
            pred_original_sample = model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
                sample / (sigma_input**2 + 1)
            )
        elif self.config.prediction_type == "sample":
            raise NotImplementedError("prediction_type not implemented yet: sample")
        else:
            raise ValueError(
                f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"
            )

        if self.state_in_first_order:
            # 2. Convert to an ODE derivative for 1st order
            derivative = (sample - pred_original_sample) / sigma_hat
            # 3. delta timestep
            dt = sigma_next - sigma_hat

            # store for 2nd order step
            self.prev_derivative = derivative
            self.dt = dt
            self.sample = sample
        else:
            # 2. 2nd order / Heun's method
            derivative = (sample - pred_original_sample) / sigma_next
            derivative = (self.prev_derivative + derivative) / 2

            # 3. take prev timestep & sample
            dt = self.dt
            sample = self.sample

            # free dt and derivative
            # Note, this puts the scheduler in "first order mode"
            self.prev_derivative = None
            self.dt = None
            self.sample = None

        prev_sample = sample + derivative * dt

        if not return_dict:
            return (prev_sample,)

        return SchedulerOutput(prev_sample=prev_sample)

    def add_noise(
        self,
        original_samples: torch.FloatTensor,
        noise: torch.FloatTensor,
        timesteps: torch.FloatTensor,
    ) -> torch.FloatTensor:
        # Make sure sigmas and timesteps have the same device and dtype as original_samples
        self.sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
        if original_samples.device.type == "mps" and torch.is_floating_point(timesteps):
            # mps does not support float64
            self.timesteps = self.timesteps.to(original_samples.device, dtype=torch.float32)
            timesteps = timesteps.to(original_samples.device, dtype=torch.float32)
        else:
            self.timesteps = self.timesteps.to(original_samples.device)
            timesteps = timesteps.to(original_samples.device)

        step_indices = [self.index_for_timestep(t) for t in timesteps]

        sigma = self.sigmas[step_indices].flatten()
        while len(sigma.shape) < len(original_samples.shape):
            sigma = sigma.unsqueeze(-1)

        noisy_samples = original_samples + noise * sigma
        return noisy_samples

    def __len__(self):
        return self.config.num_train_timesteps