diffusion.py

import torch
from torch import nn
import numpy as np
import torch.nn.functional as F
from torchvision import utils as tv_utils
from inspect import isfunction
from tqdm import tqdm


def exists(x):
    return x is not None


def default(val, d):
    if exists(val):
        return val
    return d() if isfunction(d) else d


def cycle(dl):
    while True:
        for data in dl:
            yield data


def num_to_groups(num, divisor):
    groups = num // divisor
    remainder = num % divisor
    arr = [divisor] * groups
    if remainder > 0:
        arr.append(remainder)
    return arr


def normalize_to_neg_one_to_one(img):
    return img * 2 - 1


def unnormalize_to_zero_to_one(t):
    return (t + 1) * 0.5

def extract(a, t, x_shape):
    b, *_ = t.shape
    out = a.gather(-1, t)
    return out.reshape(b, *((1,) * (len(x_shape) - 1)))


def linear_beta_schedule(timesteps):
    scale = 1000 / timesteps
    beta_start = scale * 0.0001
    beta_end = scale * 0.02
    return torch.linspace(beta_start, beta_end, timesteps, dtype=torch.float64)


def cosine_beta_schedule(timesteps, s=0.008):
    """
    cosine schedule
    as proposed in https://openreview.net/forum?id=-NEXDKk8gZ
    """
    steps = timesteps + 1
    x = torch.linspace(0, timesteps, steps, dtype=torch.float64)
    alphas_cumprod = torch.cos(
        ((x / timesteps) + s) / (1 + s) * torch.pi * 0.5) ** 2
    alphas_cumprod = alphas_cumprod / alphas_cumprod[0]
    betas = 1 - (alphas_cumprod[1:] / alphas_cumprod[:-1])
    return torch.clip(betas, 0, 0.999)


class GaussianDiffusion(nn.Module):
    def __init__(
            self,
            denoise_fn,
            *,
            image_size,
            channels=3,
            timesteps=1000,
            loss_type='l1',
            objective='pred_noise',
            beta_schedule='cosine'
    ):
        super().__init__()
        # assert not (isinstance(self, GaussianDiffusion) and denoise_fn.channels != denoise_fn.out_dim)

        self.channels = channels
        self.image_size = image_size
        self.denoise_fn = denoise_fn
        self.objective = objective

        if beta_schedule == 'linear':
            betas = linear_beta_schedule(timesteps)
        elif beta_schedule == 'cosine':
            betas = cosine_beta_schedule(timesteps)
        else:
            raise ValueError(f'unknown beta schedule {beta_schedule}')

        alphas = 1. - betas
        alphas_cumprod = torch.cumprod(alphas, axis=0)
        alphas_cumprod_prev = F.pad(alphas_cumprod[:-1], (1, 0), value=1.)

        timesteps, = betas.shape
        self.num_timesteps = int(timesteps)
        self.loss_type = loss_type

        # helper function to register buffer from float64 to float32
        def register_buffer(name, val):
            return self.register_buffer(name, val.to(torch.float32))

        register_buffer('betas', betas)
        register_buffer('alphas_cumprod', alphas_cumprod)
        register_buffer('alphas_cumprod_prev', alphas_cumprod_prev)

        # calculations for diffusion q(x_t | x_{t-1}) and others

        register_buffer('sqrt_alphas_cumprod', torch.sqrt(alphas_cumprod))
        register_buffer('sqrt_one_minus_alphas_cumprod', torch.sqrt(1. - alphas_cumprod))
        register_buffer('log_one_minus_alphas_cumprod', torch.log(1. - alphas_cumprod))
        register_buffer('sqrt_recip_alphas_cumprod', torch.sqrt(1. / alphas_cumprod))
        register_buffer('sqrt_recipm1_alphas_cumprod', torch.sqrt(1. / alphas_cumprod - 1))

        # calculations for posterior q(x_{t-1} | x_t, x_0)

        posterior_variance = betas * (1. - alphas_cumprod_prev) / (1. - alphas_cumprod)

        # above: equal to 1. / (1. / (1. - alpha_cumprod_tm1) + alpha_t / beta_t)

        register_buffer('posterior_variance', posterior_variance)

        # below: log calculation clipped because the posterior variance is 0 at the beginning of the diffusion chain

        register_buffer('posterior_log_variance_clipped', torch.log(posterior_variance.clamp(min=1e-20)))
        register_buffer('posterior_mean_coef1', betas * torch.sqrt(alphas_cumprod_prev) / (1. - alphas_cumprod))
        register_buffer('posterior_mean_coef2', (1. - alphas_cumprod_prev) * torch.sqrt(alphas) / (1. - alphas_cumprod))

    def predict_start_from_noise(self, x_t, t, noise):
        return (
                extract(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t -
                extract(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape) * noise
        )

    def q_posterior(self, x_start, x_t, t):
        posterior_mean = (
                extract(self.posterior_mean_coef1, t, x_t.shape) * x_start +
                extract(self.posterior_mean_coef2, t, x_t.shape) * x_t
        )
        posterior_variance = extract(self.posterior_variance, t, x_t.shape)
        posterior_log_variance_clipped = extract(self.posterior_log_variance_clipped, t, x_t.shape)
        return posterior_mean, posterior_variance, posterior_log_variance_clipped

    def p_mean_variance(self, x, t, clip_denoised: bool):
        model_output = self.denoise_fn(x, t, recon=True)

        if self.objective == 'pred_noise':
            x_start = self.predict_start_from_noise(x, t=t, noise=model_output)
        elif self.objective == 'pred_x0':
            x_start = model_output
        else:
            raise ValueError(f'unknown objective {self.objective}')

        if clip_denoised:
            x_start.clamp_(-1., 1.)

        model_mean, posterior_variance, posterior_log_variance = self.q_posterior(x_start=x_start, x_t=x, t=t)
        return model_mean, posterior_variance, posterior_log_variance

    @torch.no_grad()
    def p_sample(self, x, t, clip_denoised=True):
        b, *_, device = *x.shape, x.device
        model_mean, _, model_log_variance = self.p_mean_variance(x=x, t=t, clip_denoised=clip_denoised)
        noise = torch.randn_like(x)
        # no noise when t == 0
        nonzero_mask = (1 - (t == 0).float()).reshape(b, *((1,) * (len(x.shape) - 1)))
        return model_mean + nonzero_mask * (0.5 * model_log_variance).exp() * noise

    @torch.no_grad()
    def p_sample_loop(self, shape, save_video=False):
        device = self.betas.device

        b = shape[0]
        img = torch.randn(shape, device=device)
        print(f'sampling loop time step {self.num_timesteps}')
        for i in reversed(range(0, self.num_timesteps)):
            img = self.p_sample(img, torch.full((b,), i, device=device, dtype=torch.long))
            if save_video and ((i + 1) % 5 == 0 or i == 0):
                if i == 0:
                    idx = 0
                else:
                    idx = int(i // 5)
                tv_utils.save_image(unnormalize_to_zero_to_one(img), f'iter-{200-idx}.png', nrow=int(np.sqrt(b)))
        img = unnormalize_to_zero_to_one(img)
        return img

    @torch.no_grad()
    def sample(self, batch_size=16, save_video=False):
        image_size = self.image_size
        channels = self.channels
        return self.p_sample_loop((batch_size, channels, image_size, image_size), save_video=save_video)

    @torch.no_grad()
    def interpolate(self, x1, x2, t=None, lam=0.5):
        b, *_, device = *x1.shape, x1.device
        t = default(t, self.num_timesteps - 1)

        assert x1.shape == x2.shape

        t_batched = torch.stack([torch.tensor(t, device=device)] * b)
        xt1, xt2 = map(lambda x: self.q_sample(x, t=t_batched), (x1, x2))

        img = (1 - lam) * xt1 + lam * xt2
        for i in reversed(range(0, t)):
            img = self.p_sample(img, torch.full((b,), i, device=device, dtype=torch.long))

        return img

    def q_sample(self, x_start, t, noise=None):
        noise = default(noise, lambda: torch.randn_like(x_start))

        return (
                extract(self.sqrt_alphas_cumprod, t, x_start.shape) * x_start +
                extract(self.sqrt_one_minus_alphas_cumprod, t, x_start.shape) * noise
        )

    @property
    def loss_fn(self):
        if self.loss_type == 'l1':
            return F.l1_loss
        elif self.loss_type == 'l2':
            return F.mse_loss
        else:
            raise ValueError(f'invalid loss type {self.loss_type}')

    def p_losses(self, x_start, t, noise=None):
        # b, c, h, w = x_start.shape
        noise = default(noise, lambda: torch.randn_like(x_start))

        x = self.q_sample(x_start=x_start, t=t, noise=noise)
        model_out = self.denoise_fn(x, t, recon=True)

        if self.objective == 'pred_noise':
            target = noise
        elif self.objective == 'pred_x0':
            target = x_start
        else:
            raise ValueError(f'unknown objective {self.objective}')

        loss = self.loss_fn(model_out, target)
        # if model_out.shape[2] > 32:
        #     pooling = nn.MaxPool2d(2, stride=2)
        #     x_s = pooling(model_out)
        #     t_s = pooling(target)
        #     loss += self.loss_fn(x_s, t_s) * 0.2

        # if model_out.shape[2] % 3 == 0:
        #     pooling = nn.MaxPool2d(3, stride=3)
        #     x_s = pooling(model_out)
        #     t_s = pooling(target)
        #     loss += self.loss_fn(x_s, t_s) * 0.1
        return loss

    def forward(self, img):
        b, c, h, w = img.shape
        device, img_size = img.device, self.image_size
        assert h == img_size and w == img_size, f'height and width of image must be {img_size}'

        # img = normalize_to_neg_one_to_one(img)
        t = torch.randint(0, self.num_timesteps, (b,), device=device).long()
        return self.p_losses(img, t)