fastvideo/models/stable_diffusion/ddim_with_logprob_v6_2.py

# Copied from https://github.com/kvablack/ddpo-pytorch/blob/main/ddpo_pytorch/diffusers_patch/ddim_with_logprob.py, which is licensed under MIT license.

from typing import Optional, Tuple, Union

import math
import torch

from diffusers.utils.torch_utils import randn_tensor
from diffusers.schedulers.scheduling_ddim import DDIMSchedulerOutput, DDIMScheduler


def _left_broadcast(t, shape):
    assert t.ndim <= len(shape)
    return t.reshape(t.shape + (1,) * (len(shape) - t.ndim)).broadcast_to(shape)


def _get_variance(self, timestep, prev_timestep):
    ## a_t
    alpha_prod_t = torch.gather(self.alphas_cumprod, 0, timestep.cpu()).to(timestep.device)

    ## a_t-1
    alpha_prod_t_prev = torch.where(prev_timestep.cpu() >= 0,self.alphas_cumprod.gather(0, prev_timestep.cpu()),self.final_alpha_cumprod,).to(timestep.device)

    ## b_t
    beta_prod_t = 1 - alpha_prod_t

    ## b_t-1
    beta_prod_t_prev = 1 - alpha_prod_t_prev

    ## (b_t-1 / b_t) * (1 - a_t/a_t-1)
    variance = (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

    return variance


def ddim_step_with_logprob(
    self: DDIMScheduler,
    model_output: torch.FloatTensor,
    timestep: int,
    sample: torch.FloatTensor,
    eta: float = 0.0,
    use_clipped_model_output: bool = False,
    generator=None,
    prev_sample: Optional[torch.FloatTensor] = None,
) -> Union[DDIMSchedulerOutput, 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.
        eta (`float`): weight of noise for added noise in diffusion step.
        use_clipped_model_output (`bool`): if `True`, compute "corrected" `model_output` from the clipped
            predicted original sample. Necessary because predicted original sample is clipped to [-1, 1] when
            `self.config.clip_sample` is `True`. If no clipping has happened, "corrected" `model_output` would
            coincide with the one provided as input and `use_clipped_model_output` will have not effect.
        generator: random number generator.
        variance_noise (`torch.FloatTensor`): instead of generating noise for the variance using `generator`, we
            can directly provide the noise for the variance itself. This is useful for methods such as
            CycleDiffusion. (https://arxiv.org/abs/2210.05559)
        return_dict (`bool`): option for returning tuple rather than DDIMSchedulerOutput class

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

    """
    assert isinstance(self, DDIMScheduler)
    if self.num_inference_steps is None:
        raise ValueError(
            "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"
        )

    # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
    # Ideally, read DDIM paper in-detail understanding

    # Notation (<variable name> -> <name in paper>
    # - pred_noise_t -> e_theta(x_t, t)
    # - pred_original_sample -> f_theta(x_t, t) or x_0
    # - std_dev_t -> sigma_t
    # - eta -> η
    # - pred_sample_direction -> "direction pointing to x_t"
    # - pred_prev_sample -> "x_t-1"

    ## t-1
    prev_timestep = ( 
        timestep - self.config.num_train_timesteps // self.num_inference_steps
    )
    prev_timestep = torch.clamp(prev_timestep, 0, self.config.num_train_timesteps - 1)

    ## a_t
    alpha_prod_t = self.alphas_cumprod.gather(0, timestep.cpu())

    ## a_t-1
    alpha_prod_t_prev = torch.where(
        prev_timestep.cpu() >= 0,
        self.alphas_cumprod.gather(0, prev_timestep.cpu()),
        self.final_alpha_cumprod,
    )

    ## a_t  # torch.Size([4, 4, 64, 64])
    alpha_prod_t = _left_broadcast(alpha_prod_t, sample.shape).to(sample.device)

    ## a_t-1
    alpha_prod_t_prev = _left_broadcast(alpha_prod_t_prev, sample.shape).to(
        sample.device
    )

    ## b_t
    beta_prod_t = 1 - alpha_prod_t

    ## pred_x_0
    if self.config.prediction_type == "epsilon":
        pred_original_sample = (
            sample - beta_prod_t ** (0.5) * model_output
        ) / alpha_prod_t ** (0.5)
        pred_epsilon = model_output
    elif self.config.prediction_type == "sample":
        pred_original_sample = model_output
        pred_epsilon = (
            sample - alpha_prod_t ** (0.5) * pred_original_sample
        ) / beta_prod_t ** (0.5)
    elif self.config.prediction_type == "v_prediction":
        pred_original_sample = (alpha_prod_t**0.5) * sample - (
            beta_prod_t**0.5
        ) * model_output
        pred_epsilon = (alpha_prod_t**0.5) * model_output + (
            beta_prod_t**0.5
        ) * sample
    else:
        raise ValueError(
            f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
            " `v_prediction`"
        )

    # 4. 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
        )

    # 5. compute variance: "sigma_t(η)" -> see formula (16)
    # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)

    ## (b_t-1 / b_t) * (1 - a_t/a_t-1) : 0.2065
    variance = _get_variance(self, timestep, prev_timestep)

    ## std = eta * sqrt(var)
    std_dev_t = eta * variance ** (0.5)
    std_dev_t = _left_broadcast(std_dev_t, sample.shape).to(sample.device)

    if use_clipped_model_output:
        # the pred_epsilon is always re-derived from the clipped x_0 in Glide
        pred_epsilon = (
            sample - alpha_prod_t ** (0.5) * pred_original_sample
        ) / beta_prod_t ** (0.5)

    # 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
    pred_sample_direction = (1 - alpha_prod_t_prev - std_dev_t**2) ** (
        0.5
    ) * pred_epsilon

    # 7. x_t-1-less
    prev_sample_mean = (
        alpha_prod_t_prev ** (0.5) * pred_original_sample + pred_sample_direction
    )

    if prev_sample is not None and generator is not None:
        raise ValueError(
            "Cannot pass both generator and prev_sample. Please make sure that either `generator` or"
            " `prev_sample` stays `None`."
        )
    
    if prev_sample is None:
        variance_noise = randn_tensor(
            model_output.shape,
            generator=generator,
            device=model_output.device,
            dtype=model_output.dtype,
        )

        ## x_t-1 = x_t-1_mean + std * noise
        prev_sample = prev_sample_mean + std_dev_t * variance_noise
    ## x_t -> 多个 x_t-1

    # log prob of prev_sample given prev_sample_mean and std_dev_t
    log_prob = (
        -((prev_sample.detach() - prev_sample_mean) ** 2) / (2 * (std_dev_t**2))- torch.log(std_dev_t)- torch.log(torch.sqrt(2 * torch.as_tensor(math.pi)))
    )

    # mean along all but batch dimension
    # log_prob = log_prob.mean(dim=tuple(range(1, log_prob.ndim)))

    return prev_sample.type(sample.dtype), log_prob