scheduling_lms_discrete.py

# Copyright 2023 Katherine Crowson 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.
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#     http://www.apache.org/licenses/LICENSE-2.0
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# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
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import math
import warnings
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch
from scipy import integrate

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


@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete
class LMSDiscreteSchedulerOutput(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


# Copied from diffusers.schedulers.scheduling_ddpm.betas_for_alpha_bar
def betas_for_alpha_bar(num_diffusion_timesteps, max_beta=0.999):
    """
    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 LMSDiscreteScheduler(SchedulerMixin, ConfigMixin):
    """
    Linear Multistep Scheduler 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#L181

    [`~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.
        use_karras_sigmas (`bool`, *optional*, defaults to `False`):
            This parameter controls whether to use Karras sigmas (Karras et al. (2022) scheme) for step sizes in the
            noise schedule during the sampling process. If True, the sigmas will be determined according to a sequence
            of noise levels {σi} as defined in Equation (5) of the paper https://arxiv.org/pdf/2206.00364.pdf.
        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)
        timestep_spacing (`str`, default `"linspace"`):
            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,
        use_karras_sigmas: Optional[bool] = False,
        prediction_type: str = "epsilon",
        timestep_spacing: str = "linspace",
        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)
        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)

        sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
        sigmas = np.concatenate([sigmas[::-1], [0.0]]).astype(np.float32)
        self.sigmas = torch.from_numpy(sigmas)

        # setable values
        self.num_inference_steps = None
        self.use_karras_sigmas = use_karras_sigmas
        self.set_timesteps(num_train_timesteps, None)
        self.derivatives = []
        self.is_scale_input_called = False

    @property
    def init_noise_sigma(self):
        # standard deviation of the initial noise distribution
        if self.config.timestep_spacing in ["linspace", "trailing"]:
            return self.sigmas.max()

        return (self.sigmas.max() ** 2 + 1) ** 0.5

    def scale_model_input(
        self, sample: torch.FloatTensor, timestep: Union[float, torch.FloatTensor]
    ) -> torch.FloatTensor:
        """
        Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the K-LMS algorithm.

        Args:
            sample (`torch.FloatTensor`): input sample
            timestep (`float` or `torch.FloatTensor`): the current timestep in the diffusion chain

        Returns:
            `torch.FloatTensor`: scaled input sample
        """
        if isinstance(timestep, torch.Tensor):
            timestep = timestep.to(self.timesteps.device)
        step_index = (self.timesteps == timestep).nonzero().item()
        sigma = self.sigmas[step_index]
        sample = sample / ((sigma**2 + 1) ** 0.5)
        self.is_scale_input_called = True
        return sample

    def get_lms_coefficient(self, order, t, current_order):
        """
        Compute a linear multistep coefficient.

        Args:
            order (TODO):
            t (TODO):
            current_order (TODO):
        """

        def lms_derivative(tau):
            prod = 1.0
            for k in range(order):
                if current_order == k:
                    continue
                prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
            return prod

        integrated_coeff = integrate.quad(lms_derivative, self.sigmas[t], self.sigmas[t + 1], epsrel=1e-4)[0]

        return integrated_coeff

    def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = 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

        # "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, dtype=float)[
                ::-1
            ].copy()
        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(float)
            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.arange(self.config.num_train_timesteps, 0, -step_ratio)).round().copy().astype(float)
            timesteps -= 1
        else:
            raise ValueError(
                f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."
            )

        sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
        log_sigmas = np.log(sigmas)
        sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)

        if self.use_karras_sigmas:
            sigmas = self._convert_to_karras(in_sigmas=sigmas)
            timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])

        sigmas = np.concatenate([sigmas, [0.0]]).astype(np.float32)

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

        self.derivatives = []

    # copied from diffusers.schedulers.scheduling_euler_discrete._sigma_to_t
    def _sigma_to_t(self, sigma, log_sigmas):
        # get log sigma
        log_sigma = np.log(sigma)

        # get distribution
        dists = log_sigma - log_sigmas[:, np.newaxis]

        # get sigmas range
        low_idx = np.cumsum((dists >= 0), axis=0).argmax(axis=0).clip(max=log_sigmas.shape[0] - 2)
        high_idx = low_idx + 1

        low = log_sigmas[low_idx]
        high = log_sigmas[high_idx]

        # interpolate sigmas
        w = (low - log_sigma) / (low - high)
        w = np.clip(w, 0, 1)

        # transform interpolation to time range
        t = (1 - w) * low_idx + w * high_idx
        t = t.reshape(sigma.shape)
        return t

    # copied from diffusers.schedulers.scheduling_euler_discrete._convert_to_karras
    def _convert_to_karras(self, in_sigmas: torch.FloatTensor) -> torch.FloatTensor:
        """Constructs the noise schedule of Karras et al. (2022)."""

        sigma_min: float = in_sigmas[-1].item()
        sigma_max: float = in_sigmas[0].item()

        rho = 7.0  # 7.0 is the value used in the paper
        ramp = np.linspace(0, 1, self.num_inference_steps)
        min_inv_rho = sigma_min ** (1 / rho)
        max_inv_rho = sigma_max ** (1 / rho)
        sigmas = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
        return sigmas

    def step(
        self,
        model_output: torch.FloatTensor,
        timestep: Union[float, torch.FloatTensor],
        sample: torch.FloatTensor,
        order: int = 4,
        return_dict: bool = True,
    ) -> Union[LMSDiscreteSchedulerOutput, 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 (`float`): current timestep in the diffusion chain.
            sample (`torch.FloatTensor`):
                current instance of sample being created by diffusion process.
            order: coefficient for multi-step inference.
            return_dict (`bool`): option for returning tuple rather than LMSDiscreteSchedulerOutput class

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

        """
        if not self.is_scale_input_called:
            warnings.warn(
                "The `scale_model_input` function should be called before `step` to ensure correct denoising. "
                "See `StableDiffusionPipeline` for a usage example."
            )

        if isinstance(timestep, torch.Tensor):
            timestep = timestep.to(self.timesteps.device)
        step_index = (self.timesteps == timestep).nonzero().item()
        sigma = self.sigmas[step_index]

        # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
        if self.config.prediction_type == "epsilon":
            pred_original_sample = sample - sigma * model_output
        elif self.config.prediction_type == "v_prediction":
            # * c_out + input * c_skip
            pred_original_sample = model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
        elif self.config.prediction_type == "sample":
            pred_original_sample = model_output
        else:
            raise ValueError(
                f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"
            )

        # 2. Convert to an ODE derivative
        derivative = (sample - pred_original_sample) / sigma
        self.derivatives.append(derivative)
        if len(self.derivatives) > order:
            self.derivatives.pop(0)

        # 3. Compute linear multistep coefficients
        order = min(step_index + 1, order)
        lms_coeffs = [self.get_lms_coefficient(order, step_index, curr_order) for curr_order in range(order)]

        # 4. Compute previous sample based on the derivatives path
        prev_sample = sample + sum(
            coeff * derivative for coeff, derivative in zip(lms_coeffs, reversed(self.derivatives))
        )

        if not return_dict:
            return (prev_sample,)

        return LMSDiscreteSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_sample)

    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.add_noise
    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
        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
            schedule_timesteps = self.timesteps.to(original_samples.device, dtype=torch.float32)
            timesteps = timesteps.to(original_samples.device, dtype=torch.float32)
        else:
            schedule_timesteps = self.timesteps.to(original_samples.device)
            timesteps = timesteps.to(original_samples.device)

        step_indices = [(schedule_timesteps == t).nonzero().item() for t in timesteps]

        sigma = 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