ddim_inversion_utils.py

# adapted and updated from https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_ddim.py

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

import numpy as np
import torch
#import matplotlib.pyplot as plt
from tqdm import tqdm as tqdm1
from tqdm.auto import tqdm
from PIL import Image

from diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.utils import BaseOutput, deprecate
from diffusers.schedulers.scheduling_utils import SchedulerMixin



def betas_for_alpha_bar(num_diffusion_timesteps, max_beta=0.999) -> torch.Tensor:
  
    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)


def DDIM_efficient_feed_forward(latent, model, ddim_scheduler):
    for i, t in enumerate(tqdm1(ddim_scheduler.timesteps)):
        t1 = (torch.ones(1) * t) .cuda()#.to(x_t.device)
        with torch.no_grad():      
            if i == 0:                
                noise_pred = model(latent, t1)   
            else:  
                noise_pred = model(x_t, t1) #.sample    
        noise_pred = noise_pred[:, :3]         

        if i == 0:
            x_t = ddim_scheduler.step(noise_pred, t, latent, return_dict=True, use_clipped_model_output=True)
        else:
            x_t = ddim_scheduler.step(noise_pred, t, x_t, return_dict=True, use_clipped_model_output=True)
    return x_t

class DDIMScheduler(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[np.ndarray] = None,
        clip_sample: bool = True,
        set_alpha_to_one: bool = True,
        steps_offset: int = 0,
    ):
        if trained_betas is not None:
            self.betas = torch.from_numpy(trained_betas)
        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)

        # At every step in ddim, we are looking into the previous alphas_cumprod
        # For the final step, there is no previous alphas_cumprod because we are already at 0
        # `set_alpha_to_one` decides whether we set this parameter simply to one or
        # whether we use the final alpha of the "non-previous" one.
        self.final_alpha_cumprod = torch.tensor(1.0) if set_alpha_to_one else self.alphas_cumprod[0]

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

        # setable values
        self.num_inference_steps = None
        self.timesteps = torch.from_numpy(np.arange(0, num_train_timesteps)[::-1].copy().astype(np.int64))

    def _get_variance(self, timestep, prev_timestep):
        alpha_prod_t = self.alphas_cumprod[timestep]
        alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
        beta_prod_t = 1 - alpha_prod_t
        beta_prod_t_prev = 1 - alpha_prod_t_prev

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

        return variance

    def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
        """
        Sets the discrete 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.
        """
        self.num_inference_steps = num_inference_steps
        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)
        self.timesteps = torch.from_numpy(timesteps).to(device)
        self.timesteps += self.config.steps_offset
        
    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 step(
        self,
        model_output: torch.FloatTensor,
        timestep: int,
        sample: torch.FloatTensor,
        eta: float = 0.0,
        use_clipped_model_output: bool = False,
        generator=None,
        return_dict: bool = True,
    ) ->  torch.FloatTensor:
        """
        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`): TODO
            generator: random number generator.
            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.

        """
        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"

        # 1. get previous step value (=t-1)
        prev_timestep = timestep - self.config.num_train_timesteps // self.num_inference_steps

        # 2. compute alphas, betas
        alpha_prod_t = self.alphas_cumprod[timestep]
        alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod

        beta_prod_t = 1 - alpha_prod_t

        # 3. compute predicted original sample from predicted noise also called
        # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)

        # 4. Clip "predicted x_0"
        if self.config.clip_sample:
            pred_original_sample = torch.clamp(pred_original_sample, -1, 1)

        # 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)
        variance = self._get_variance(timestep, prev_timestep)
        std_dev_t = eta * variance ** (0.5)

        if use_clipped_model_output:
            # the model_output is always re-derived from the clipped x_0 in Glide
            model_output = (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) * model_output

        # 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        prev_sample = alpha_prod_t_prev ** (0.5) * pred_original_sample + pred_sample_direction

        if eta > 0:
            device = model_output.device if torch.is_tensor(model_output) else "cpu"
            noise = torch.randn(model_output.shape, generator=generator).to(device)
            variance = self._get_variance(timestep, prev_timestep) ** (0.5) * eta * noise

            prev_sample = prev_sample + variance

       
        return prev_sample


   
    def add_noise(
        self,
        original_samples: torch.FloatTensor,
        noise: torch.FloatTensor,
        timesteps: torch.IntTensor,
    ) -> torch.FloatTensor:
        if self.alphas_cumprod.device != original_samples.device:
            self.alphas_cumprod = self.alphas_cumprod.to(original_samples.device)
        if timesteps.device != original_samples.device:
            timesteps = timesteps.to(original_samples.device)

        sqrt_alpha_prod = self.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 - self.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 __len__(self):
        return self.config.num_train_timesteps