scheduler/i2sb_scheduler.py

# Copyright 2024 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 List, Optional, Tuple, Union

import numpy as np
import torch

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


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

    prev_sample: torch.Tensor
    pred_original_sample: Optional[torch.Tensor] = 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_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)


# Copied from diffusers.schedulers.scheduling_ddim.rescale_zero_terminal_snr
def rescale_zero_terminal_snr(betas):
    """
    Rescales betas to have zero terminal SNR Based on https://arxiv.org/pdf/2305.08891.pdf (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


def compute_gaussian_product_coef(sigma1, sigma2):
    """ Given p1 = N(x_t|x_0, sigma_1**2) and p2 = N(x_t|x_1, sigma_2**2)
        return p1 * p2 = N(x_t| coef1 * x0 + coef2 * x1, var) """

    denom = sigma1**2 + sigma2**2
    coef1 = sigma2**2 / denom
    coef2 = sigma1**2 / denom
    var = (sigma1**2 * sigma2**2) / denom
    return coef1, coef2, var


class I2SBScheduler(SchedulerMixin, ConfigMixin):

    @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,
        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)
        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} is not implemented for {self.__class__}")

        # Rescale for zero SNR
        if rescale_betas_zero_snr:
            self.betas = rescale_zero_terminal_snr(self.betas)

        std_fwd = torch.sqrt(torch.cumsum(self.betas, 0))
        std_bwd = torch.sqrt(torch.flip(
            torch.cumsum(torch.flip(self.betas, dims=[0]), 0), dims=[0]))
        mu_x0, mu_x1, var = compute_gaussian_product_coef(std_fwd, std_bwd)
        std_sb = torch.sqrt(var)
        self.std_fwd = std_fwd
        self.std_bwd = std_bwd
        self.std_sb = std_sb
        self.mu_x0 = mu_x0
        self.mu_x1 = mu_x1

        # 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.Tensor, timestep: Optional[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 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 (to be run before inference).

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

        if dtype not in (torch.float32, torch.float64):
            # upcast for quantile calculation, and clamp not implemented for cpu half
            sample = sample.float()

        # 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]
        # (batch_size, 1) because clamp will broadcast along dim=0
        s = s.unsqueeze(1)
        # "we threshold xt0 to the range [-s, s] and then divide by s"
        sample = torch.clamp(sample, -s, s) / s

        sample = sample.reshape(batch_size, channels, *remaining_dims)
        sample = sample.to(dtype)

        return sample

    def step(
        self,
        model_output: torch.Tensor,
        timestep: int,
        sample: torch.Tensor,
        is_ode: bool = False,
        generator=None,
        return_dict: bool = True,
    ) -> Union[DDPMSchedulerOutput, 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 (`float`):
                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`, *optional*):
                A random number generator.
            return_dict (`bool`, *optional*, defaults to `True`):
                Whether or not to return a [`~schedulers.scheduling_ddpm.DDPMSchedulerOutput`] or `tuple`.

        Returns:
            [`~schedulers.scheduling_ddpm.DDPMSchedulerOutput`] or `tuple`:
                If return_dict is `True`, [`~schedulers.scheduling_ddpm.DDPMSchedulerOutput`] is returned, otherwise a
                tuple is returned where 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

        std_fwd_list = self.std_fwd.to(device=sample.device)
        std_fwd = std_fwd_list[t]
        std_fwd_prev = std_fwd_list[prev_t]
        std_delta = (std_fwd**2 - std_fwd_prev**2).sqrt()

        pred_original_sample = sample - std_fwd * model_output

        # 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
            )

        mu_x0, mu_xt, var = compute_gaussian_product_coef(
            std_fwd_prev, std_delta)
        pred_prev_sample = mu_x0 * pred_original_sample + mu_xt * sample

        # 6. Add noise
        variance_noise = 0
        if t > 0 and not is_ode:
            device = model_output.device
            variance_noise = randn_tensor(
                model_output.shape, generator=generator, device=device, dtype=model_output.dtype
            ) * var.sqrt()

        pred_prev_sample = pred_prev_sample + variance_noise

        # from torchvision.utils import save_image
        # img_cat = torch.cat((xn, pred_original_sample, pred_prev_sample), 2)
        # save_image((img_cat + 1) / 2, f'tmp/tmp_{t.item()}.png')

        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,
        x0: torch.Tensor,
        x1: torch.Tensor,
        timesteps: torch.IntTensor,
        is_ode: bool = False,
        noise=None
    ) -> torch.Tensor:
        mu_x0 = self.mu_x0.to(device=x0.device)
        mu_x0 = mu_x0[timesteps]
        mu_x1 = self.mu_x1.to(device=x0.device)
        mu_x1 = mu_x1[timesteps]
        std_sb = self.std_sb.to(device=x0.device)
        std_sb = std_sb[timesteps]
        while len(mu_x0.shape) < len(x0.shape):
            mu_x0 = mu_x0.unsqueeze(-1)
            mu_x1 = mu_x1.unsqueeze(-1)
            std_sb = std_sb.unsqueeze(-1)

        xt = mu_x0 * x0 + mu_x1 * x1
        if not is_ode:
            if noise is None:
                noise = torch.randn_like(xt)
            xt = xt + std_sb * noise
        return xt

    def get_velocity(self, sample: torch.Tensor, noise: torch.Tensor, timesteps: torch.IntTensor) -> torch.Tensor:
        raise NotImplementedError
        # 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 compute_label(self, timesteps, x0, xt):
        std_fwd = self.std_fwd.to(device=x0.device)
        std_fwd = std_fwd[timesteps]
        while len(std_fwd.shape) < len(x0.shape):
            std_fwd = std_fwd.unsqueeze(-1)
        label = (xt - x0) / std_fwd
        return label

    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