740 lines
33 KiB
Python
740 lines
33 KiB
Python
import math
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from scipy import integrate
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import torch
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from torch import nn
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import torchsde
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from tqdm.auto import trange, tqdm
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from . import utils
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def append_zero(x):
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return torch.cat([x, x.new_zeros([1])])
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def get_sigmas_karras(n, sigma_min, sigma_max, rho=7., device='cpu'):
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"""Constructs the noise schedule of Karras et al. (2022)."""
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ramp = torch.linspace(0, 1, n, device=device)
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min_inv_rho = sigma_min ** (1 / rho)
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max_inv_rho = sigma_max ** (1 / rho)
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sigmas = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
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return append_zero(sigmas).to(device)
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def get_sigmas_exponential(n, sigma_min, sigma_max, device='cpu'):
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"""Constructs an exponential noise schedule."""
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sigmas = torch.linspace(math.log(sigma_max), math.log(sigma_min), n, device=device).exp()
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return append_zero(sigmas)
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def get_sigmas_polyexponential(n, sigma_min, sigma_max, rho=1., device='cpu'):
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"""Constructs an polynomial in log sigma noise schedule."""
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ramp = torch.linspace(1, 0, n, device=device) ** rho
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sigmas = torch.exp(ramp * (math.log(sigma_max) - math.log(sigma_min)) + math.log(sigma_min))
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return append_zero(sigmas)
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def get_sigmas_vp(n, beta_d=19.9, beta_min=0.1, eps_s=1e-3, device='cpu'):
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"""Constructs a continuous VP noise schedule."""
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t = torch.linspace(1, eps_s, n, device=device)
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sigmas = torch.sqrt(torch.exp(beta_d * t ** 2 / 2 + beta_min * t) - 1)
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return append_zero(sigmas)
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def to_d(x, sigma, denoised):
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"""Converts a denoiser output to a Karras ODE derivative."""
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return (x - denoised) / utils.append_dims(sigma, x.ndim)
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def get_ancestral_step(sigma_from, sigma_to, eta=1.):
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"""Calculates the noise level (sigma_down) to step down to and the amount
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of noise to add (sigma_up) when doing an ancestral sampling step."""
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if not eta:
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return sigma_to, 0.
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sigma_up = min(sigma_to, eta * (sigma_to ** 2 * (sigma_from ** 2 - sigma_to ** 2) / sigma_from ** 2) ** 0.5)
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sigma_down = (sigma_to ** 2 - sigma_up ** 2) ** 0.5
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return sigma_down, sigma_up
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def default_noise_sampler(x):
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return lambda sigma, sigma_next: torch.randn_like(x)
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class BatchedBrownianTree:
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"""A wrapper around torchsde.BrownianTree that enables batches of entropy."""
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def __init__(self, x, t0, t1, seed=None, **kwargs):
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self.cpu_tree = True
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if "cpu" in kwargs:
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self.cpu_tree = kwargs.pop("cpu")
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t0, t1, self.sign = self.sort(t0, t1)
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w0 = kwargs.get('w0', torch.zeros_like(x))
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if seed is None:
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seed = torch.randint(0, 2 ** 63 - 1, []).item()
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self.batched = True
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try:
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assert len(seed) == x.shape[0]
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w0 = w0[0]
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except TypeError:
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seed = [seed]
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self.batched = False
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if self.cpu_tree:
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self.trees = [torchsde.BrownianTree(t0.cpu(), w0.cpu(), t1.cpu(), entropy=s, **kwargs) for s in seed]
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else:
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self.trees = [torchsde.BrownianTree(t0, w0, t1, entropy=s, **kwargs) for s in seed]
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@staticmethod
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def sort(a, b):
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return (a, b, 1) if a < b else (b, a, -1)
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def __call__(self, t0, t1):
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t0, t1, sign = self.sort(t0, t1)
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if self.cpu_tree:
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w = torch.stack([tree(t0.cpu().float(), t1.cpu().float()).to(t0.dtype).to(t0.device) for tree in self.trees]) * (self.sign * sign)
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else:
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w = torch.stack([tree(t0, t1) for tree in self.trees]) * (self.sign * sign)
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return w if self.batched else w[0]
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class BrownianTreeNoiseSampler:
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"""A noise sampler backed by a torchsde.BrownianTree.
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Args:
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x (Tensor): The tensor whose shape, device and dtype to use to generate
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random samples.
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sigma_min (float): The low end of the valid interval.
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sigma_max (float): The high end of the valid interval.
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seed (int or List[int]): The random seed. If a list of seeds is
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supplied instead of a single integer, then the noise sampler will
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use one BrownianTree per batch item, each with its own seed.
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transform (callable): A function that maps sigma to the sampler's
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internal timestep.
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"""
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def __init__(self, x, sigma_min, sigma_max, seed=None, transform=lambda x: x, cpu=False):
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self.transform = transform
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t0, t1 = self.transform(torch.as_tensor(sigma_min)), self.transform(torch.as_tensor(sigma_max))
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self.tree = BatchedBrownianTree(x, t0, t1, seed, cpu=cpu)
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def __call__(self, sigma, sigma_next):
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t0, t1 = self.transform(torch.as_tensor(sigma)), self.transform(torch.as_tensor(sigma_next))
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return self.tree(t0, t1) / (t1 - t0).abs().sqrt()
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@torch.no_grad()
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def sample_euler(model, x, sigmas, extra_args=None, callback=None, disable=None, s_churn=0., s_tmin=0., s_tmax=float('inf'), s_noise=1.):
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"""Implements Algorithm 2 (Euler steps) from Karras et al. (2022)."""
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extra_args = {} if extra_args is None else extra_args
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s_in = x.new_ones([x.shape[0]])
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for i in trange(len(sigmas) - 1, disable=disable):
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gamma = min(s_churn / (len(sigmas) - 1), 2 ** 0.5 - 1) if s_tmin <= sigmas[i] <= s_tmax else 0.
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sigma_hat = sigmas[i] * (gamma + 1)
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if gamma > 0:
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eps = torch.randn_like(x) * s_noise
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x = x + eps * (sigma_hat ** 2 - sigmas[i] ** 2) ** 0.5
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denoised = model(x, sigma_hat * s_in, **extra_args)
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d = to_d(x, sigma_hat, denoised)
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if callback is not None:
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callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigma_hat, 'denoised': denoised})
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dt = sigmas[i + 1] - sigma_hat
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# Euler method
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x = x + d * dt
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return x
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@torch.no_grad()
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def sample_euler_ancestral(model, x, sigmas, extra_args=None, callback=None, disable=None, eta=1., s_noise=1., noise_sampler=None):
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"""Ancestral sampling with Euler method steps."""
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extra_args = {} if extra_args is None else extra_args
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noise_sampler = default_noise_sampler(x) if noise_sampler is None else noise_sampler
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s_in = x.new_ones([x.shape[0]])
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for i in trange(len(sigmas) - 1, disable=disable):
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denoised = model(x, sigmas[i] * s_in, **extra_args)
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sigma_down, sigma_up = get_ancestral_step(sigmas[i], sigmas[i + 1], eta=eta)
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if callback is not None:
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callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigmas[i], 'denoised': denoised})
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d = to_d(x, sigmas[i], denoised)
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# Euler method
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dt = sigma_down - sigmas[i]
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x = x + d * dt
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if sigmas[i + 1] > 0:
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x = x + noise_sampler(sigmas[i], sigmas[i + 1]) * s_noise * sigma_up
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return x
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@torch.no_grad()
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def sample_heun(model, x, sigmas, extra_args=None, callback=None, disable=None, s_churn=0., s_tmin=0., s_tmax=float('inf'), s_noise=1.):
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"""Implements Algorithm 2 (Heun steps) from Karras et al. (2022)."""
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extra_args = {} if extra_args is None else extra_args
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s_in = x.new_ones([x.shape[0]])
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for i in trange(len(sigmas) - 1, disable=disable):
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gamma = min(s_churn / (len(sigmas) - 1), 2 ** 0.5 - 1) if s_tmin <= sigmas[i] <= s_tmax else 0.
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sigma_hat = sigmas[i] * (gamma + 1)
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if gamma > 0:
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eps = torch.randn_like(x) * s_noise
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x = x + eps * (sigma_hat ** 2 - sigmas[i] ** 2) ** 0.5
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denoised = model(x, sigma_hat * s_in, **extra_args)
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d = to_d(x, sigma_hat, denoised)
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if callback is not None:
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callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigma_hat, 'denoised': denoised})
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dt = sigmas[i + 1] - sigma_hat
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if sigmas[i + 1] == 0:
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# Euler method
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x = x + d * dt
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else:
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# Heun's method
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x_2 = x + d * dt
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denoised_2 = model(x_2, sigmas[i + 1] * s_in, **extra_args)
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d_2 = to_d(x_2, sigmas[i + 1], denoised_2)
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d_prime = (d + d_2) / 2
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x = x + d_prime * dt
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return x
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@torch.no_grad()
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def sample_dpm_2(model, x, sigmas, extra_args=None, callback=None, disable=None, s_churn=0., s_tmin=0., s_tmax=float('inf'), s_noise=1.):
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"""A sampler inspired by DPM-Solver-2 and Algorithm 2 from Karras et al. (2022)."""
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extra_args = {} if extra_args is None else extra_args
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s_in = x.new_ones([x.shape[0]])
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for i in trange(len(sigmas) - 1, disable=disable):
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gamma = min(s_churn / (len(sigmas) - 1), 2 ** 0.5 - 1) if s_tmin <= sigmas[i] <= s_tmax else 0.
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sigma_hat = sigmas[i] * (gamma + 1)
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if gamma > 0:
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eps = torch.randn_like(x) * s_noise
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x = x + eps * (sigma_hat ** 2 - sigmas[i] ** 2) ** 0.5
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denoised = model(x, sigma_hat * s_in, **extra_args)
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d = to_d(x, sigma_hat, denoised)
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if callback is not None:
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callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigma_hat, 'denoised': denoised})
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if sigmas[i + 1] == 0:
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# Euler method
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dt = sigmas[i + 1] - sigma_hat
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x = x + d * dt
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else:
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# DPM-Solver-2
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sigma_mid = sigma_hat.log().lerp(sigmas[i + 1].log(), 0.5).exp()
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dt_1 = sigma_mid - sigma_hat
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dt_2 = sigmas[i + 1] - sigma_hat
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x_2 = x + d * dt_1
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denoised_2 = model(x_2, sigma_mid * s_in, **extra_args)
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d_2 = to_d(x_2, sigma_mid, denoised_2)
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x = x + d_2 * dt_2
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return x
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@torch.no_grad()
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def sample_dpm_2_ancestral(model, x, sigmas, extra_args=None, callback=None, disable=None, eta=1., s_noise=1., noise_sampler=None):
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"""Ancestral sampling with DPM-Solver second-order steps."""
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extra_args = {} if extra_args is None else extra_args
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noise_sampler = default_noise_sampler(x) if noise_sampler is None else noise_sampler
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s_in = x.new_ones([x.shape[0]])
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for i in trange(len(sigmas) - 1, disable=disable):
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denoised = model(x, sigmas[i] * s_in, **extra_args)
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sigma_down, sigma_up = get_ancestral_step(sigmas[i], sigmas[i + 1], eta=eta)
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if callback is not None:
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callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigmas[i], 'denoised': denoised})
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d = to_d(x, sigmas[i], denoised)
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if sigma_down == 0:
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# Euler method
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dt = sigma_down - sigmas[i]
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x = x + d * dt
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else:
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# DPM-Solver-2
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sigma_mid = sigmas[i].log().lerp(sigma_down.log(), 0.5).exp()
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dt_1 = sigma_mid - sigmas[i]
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dt_2 = sigma_down - sigmas[i]
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x_2 = x + d * dt_1
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denoised_2 = model(x_2, sigma_mid * s_in, **extra_args)
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d_2 = to_d(x_2, sigma_mid, denoised_2)
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x = x + d_2 * dt_2
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x = x + noise_sampler(sigmas[i], sigmas[i + 1]) * s_noise * sigma_up
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return x
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def linear_multistep_coeff(order, t, i, j):
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if order - 1 > i:
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raise ValueError(f'Order {order} too high for step {i}')
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def fn(tau):
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prod = 1.
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for k in range(order):
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if j == k:
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continue
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prod *= (tau - t[i - k]) / (t[i - j] - t[i - k])
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return prod
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return integrate.quad(fn, t[i], t[i + 1], epsrel=1e-4)[0]
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@torch.no_grad()
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def sample_lms(model, x, sigmas, extra_args=None, callback=None, disable=None, order=4):
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extra_args = {} if extra_args is None else extra_args
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s_in = x.new_ones([x.shape[0]])
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sigmas_cpu = sigmas.detach().cpu().numpy()
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ds = []
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for i in trange(len(sigmas) - 1, disable=disable):
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denoised = model(x, sigmas[i] * s_in, **extra_args)
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d = to_d(x, sigmas[i], denoised)
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ds.append(d)
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if len(ds) > order:
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ds.pop(0)
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if callback is not None:
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callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigmas[i], 'denoised': denoised})
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cur_order = min(i + 1, order)
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coeffs = [linear_multistep_coeff(cur_order, sigmas_cpu, i, j) for j in range(cur_order)]
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x = x + sum(coeff * d for coeff, d in zip(coeffs, reversed(ds)))
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return x
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class PIDStepSizeController:
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"""A PID controller for ODE adaptive step size control."""
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def __init__(self, h, pcoeff, icoeff, dcoeff, order=1, accept_safety=0.81, eps=1e-8):
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self.h = h
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self.b1 = (pcoeff + icoeff + dcoeff) / order
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self.b2 = -(pcoeff + 2 * dcoeff) / order
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self.b3 = dcoeff / order
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self.accept_safety = accept_safety
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self.eps = eps
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self.errs = []
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def limiter(self, x):
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return 1 + math.atan(x - 1)
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def propose_step(self, error):
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inv_error = 1 / (float(error) + self.eps)
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if not self.errs:
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self.errs = [inv_error, inv_error, inv_error]
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self.errs[0] = inv_error
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factor = self.errs[0] ** self.b1 * self.errs[1] ** self.b2 * self.errs[2] ** self.b3
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factor = self.limiter(factor)
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accept = factor >= self.accept_safety
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if accept:
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self.errs[2] = self.errs[1]
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self.errs[1] = self.errs[0]
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self.h *= factor
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return accept
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class DPMSolver(nn.Module):
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"""DPM-Solver. See https://arxiv.org/abs/2206.00927."""
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def __init__(self, model, extra_args=None, eps_callback=None, info_callback=None):
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super().__init__()
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self.model = model
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self.extra_args = {} if extra_args is None else extra_args
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self.eps_callback = eps_callback
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self.info_callback = info_callback
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def t(self, sigma):
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return -sigma.log()
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def sigma(self, t):
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return t.neg().exp()
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def eps(self, eps_cache, key, x, t, *args, **kwargs):
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if key in eps_cache:
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return eps_cache[key], eps_cache
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sigma = self.sigma(t) * x.new_ones([x.shape[0]])
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eps = (x - self.model(x, sigma, *args, **self.extra_args, **kwargs)) / self.sigma(t)
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if self.eps_callback is not None:
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self.eps_callback()
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return eps, {key: eps, **eps_cache}
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def dpm_solver_1_step(self, x, t, t_next, eps_cache=None):
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eps_cache = {} if eps_cache is None else eps_cache
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h = t_next - t
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eps, eps_cache = self.eps(eps_cache, 'eps', x, t)
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x_1 = x - self.sigma(t_next) * h.expm1() * eps
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return x_1, eps_cache
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def dpm_solver_2_step(self, x, t, t_next, r1=1 / 2, eps_cache=None):
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eps_cache = {} if eps_cache is None else eps_cache
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h = t_next - t
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eps, eps_cache = self.eps(eps_cache, 'eps', x, t)
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s1 = t + r1 * h
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u1 = x - self.sigma(s1) * (r1 * h).expm1() * eps
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eps_r1, eps_cache = self.eps(eps_cache, 'eps_r1', u1, s1)
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x_2 = x - self.sigma(t_next) * h.expm1() * eps - self.sigma(t_next) / (2 * r1) * h.expm1() * (eps_r1 - eps)
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return x_2, eps_cache
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def dpm_solver_3_step(self, x, t, t_next, r1=1 / 3, r2=2 / 3, eps_cache=None):
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eps_cache = {} if eps_cache is None else eps_cache
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h = t_next - t
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eps, eps_cache = self.eps(eps_cache, 'eps', x, t)
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s1 = t + r1 * h
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s2 = t + r2 * h
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u1 = x - self.sigma(s1) * (r1 * h).expm1() * eps
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eps_r1, eps_cache = self.eps(eps_cache, 'eps_r1', u1, s1)
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u2 = x - self.sigma(s2) * (r2 * h).expm1() * eps - self.sigma(s2) * (r2 / r1) * ((r2 * h).expm1() / (r2 * h) - 1) * (eps_r1 - eps)
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eps_r2, eps_cache = self.eps(eps_cache, 'eps_r2', u2, s2)
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x_3 = x - self.sigma(t_next) * h.expm1() * eps - self.sigma(t_next) / r2 * (h.expm1() / h - 1) * (eps_r2 - eps)
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return x_3, eps_cache
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def dpm_solver_fast(self, x, t_start, t_end, nfe, eta=0., s_noise=1., noise_sampler=None):
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noise_sampler = default_noise_sampler(x) if noise_sampler is None else noise_sampler
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if not t_end > t_start and eta:
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raise ValueError('eta must be 0 for reverse sampling')
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m = math.floor(nfe / 3) + 1
|
|
ts = torch.linspace(t_start, t_end, m + 1, device=x.device)
|
|
|
|
if nfe % 3 == 0:
|
|
orders = [3] * (m - 2) + [2, 1]
|
|
else:
|
|
orders = [3] * (m - 1) + [nfe % 3]
|
|
|
|
for i in range(len(orders)):
|
|
eps_cache = {}
|
|
t, t_next = ts[i], ts[i + 1]
|
|
if eta:
|
|
sd, su = get_ancestral_step(self.sigma(t), self.sigma(t_next), eta)
|
|
t_next_ = torch.minimum(t_end, self.t(sd))
|
|
su = (self.sigma(t_next) ** 2 - self.sigma(t_next_) ** 2) ** 0.5
|
|
else:
|
|
t_next_, su = t_next, 0.
|
|
|
|
eps, eps_cache = self.eps(eps_cache, 'eps', x, t)
|
|
denoised = x - self.sigma(t) * eps
|
|
if self.info_callback is not None:
|
|
self.info_callback({'x': x, 'i': i, 't': ts[i], 't_up': t, 'denoised': denoised})
|
|
|
|
if orders[i] == 1:
|
|
x, eps_cache = self.dpm_solver_1_step(x, t, t_next_, eps_cache=eps_cache)
|
|
elif orders[i] == 2:
|
|
x, eps_cache = self.dpm_solver_2_step(x, t, t_next_, eps_cache=eps_cache)
|
|
else:
|
|
x, eps_cache = self.dpm_solver_3_step(x, t, t_next_, eps_cache=eps_cache)
|
|
|
|
x = x + su * s_noise * noise_sampler(self.sigma(t), self.sigma(t_next))
|
|
|
|
return x
|
|
|
|
def dpm_solver_adaptive(self, x, t_start, t_end, order=3, rtol=0.05, atol=0.0078, h_init=0.05, pcoeff=0., icoeff=1., dcoeff=0., accept_safety=0.81, eta=0., s_noise=1., noise_sampler=None):
|
|
noise_sampler = default_noise_sampler(x) if noise_sampler is None else noise_sampler
|
|
if order not in {2, 3}:
|
|
raise ValueError('order should be 2 or 3')
|
|
forward = t_end > t_start
|
|
if not forward and eta:
|
|
raise ValueError('eta must be 0 for reverse sampling')
|
|
h_init = abs(h_init) * (1 if forward else -1)
|
|
atol = torch.tensor(atol)
|
|
rtol = torch.tensor(rtol)
|
|
s = t_start
|
|
x_prev = x
|
|
accept = True
|
|
pid = PIDStepSizeController(h_init, pcoeff, icoeff, dcoeff, 1.5 if eta else order, accept_safety)
|
|
info = {'steps': 0, 'nfe': 0, 'n_accept': 0, 'n_reject': 0}
|
|
|
|
while s < t_end - 1e-5 if forward else s > t_end + 1e-5:
|
|
eps_cache = {}
|
|
t = torch.minimum(t_end, s + pid.h) if forward else torch.maximum(t_end, s + pid.h)
|
|
if eta:
|
|
sd, su = get_ancestral_step(self.sigma(s), self.sigma(t), eta)
|
|
t_ = torch.minimum(t_end, self.t(sd))
|
|
su = (self.sigma(t) ** 2 - self.sigma(t_) ** 2) ** 0.5
|
|
else:
|
|
t_, su = t, 0.
|
|
|
|
eps, eps_cache = self.eps(eps_cache, 'eps', x, s)
|
|
denoised = x - self.sigma(s) * eps
|
|
|
|
if order == 2:
|
|
x_low, eps_cache = self.dpm_solver_1_step(x, s, t_, eps_cache=eps_cache)
|
|
x_high, eps_cache = self.dpm_solver_2_step(x, s, t_, eps_cache=eps_cache)
|
|
else:
|
|
x_low, eps_cache = self.dpm_solver_2_step(x, s, t_, r1=1 / 3, eps_cache=eps_cache)
|
|
x_high, eps_cache = self.dpm_solver_3_step(x, s, t_, eps_cache=eps_cache)
|
|
delta = torch.maximum(atol, rtol * torch.maximum(x_low.abs(), x_prev.abs()))
|
|
error = torch.linalg.norm((x_low - x_high) / delta) / x.numel() ** 0.5
|
|
accept = pid.propose_step(error)
|
|
if accept:
|
|
x_prev = x_low
|
|
x = x_high + su * s_noise * noise_sampler(self.sigma(s), self.sigma(t))
|
|
s = t
|
|
info['n_accept'] += 1
|
|
else:
|
|
info['n_reject'] += 1
|
|
info['nfe'] += order
|
|
info['steps'] += 1
|
|
|
|
if self.info_callback is not None:
|
|
self.info_callback({'x': x, 'i': info['steps'] - 1, 't': s, 't_up': s, 'denoised': denoised, 'error': error, 'h': pid.h, **info})
|
|
|
|
return x, info
|
|
|
|
|
|
@torch.no_grad()
|
|
def sample_dpm_fast(model, x, sigma_min, sigma_max, n, extra_args=None, callback=None, disable=None, eta=0., s_noise=1., noise_sampler=None):
|
|
"""DPM-Solver-Fast (fixed step size). See https://arxiv.org/abs/2206.00927."""
|
|
if sigma_min <= 0 or sigma_max <= 0:
|
|
raise ValueError('sigma_min and sigma_max must not be 0')
|
|
with tqdm(total=n, disable=disable) as pbar:
|
|
dpm_solver = DPMSolver(model, extra_args, eps_callback=pbar.update)
|
|
if callback is not None:
|
|
dpm_solver.info_callback = lambda info: callback({'sigma': dpm_solver.sigma(info['t']), 'sigma_hat': dpm_solver.sigma(info['t_up']), **info})
|
|
return dpm_solver.dpm_solver_fast(x, dpm_solver.t(torch.tensor(sigma_max)), dpm_solver.t(torch.tensor(sigma_min)), n, eta, s_noise, noise_sampler)
|
|
|
|
|
|
@torch.no_grad()
|
|
def sample_dpm_adaptive(model, x, sigma_min, sigma_max, extra_args=None, callback=None, disable=None, order=3, rtol=0.05, atol=0.0078, h_init=0.05, pcoeff=0., icoeff=1., dcoeff=0., accept_safety=0.81, eta=0., s_noise=1., noise_sampler=None, return_info=False):
|
|
"""DPM-Solver-12 and 23 (adaptive step size). See https://arxiv.org/abs/2206.00927."""
|
|
if sigma_min <= 0 or sigma_max <= 0:
|
|
raise ValueError('sigma_min and sigma_max must not be 0')
|
|
with tqdm(disable=disable) as pbar:
|
|
dpm_solver = DPMSolver(model, extra_args, eps_callback=pbar.update)
|
|
if callback is not None:
|
|
dpm_solver.info_callback = lambda info: callback({'sigma': dpm_solver.sigma(info['t']), 'sigma_hat': dpm_solver.sigma(info['t_up']), **info})
|
|
x, info = dpm_solver.dpm_solver_adaptive(x, dpm_solver.t(torch.tensor(sigma_max)), dpm_solver.t(torch.tensor(sigma_min)), order, rtol, atol, h_init, pcoeff, icoeff, dcoeff, accept_safety, eta, s_noise, noise_sampler)
|
|
if return_info:
|
|
return x, info
|
|
return x
|
|
|
|
|
|
@torch.no_grad()
|
|
def sample_dpmpp_2s_ancestral(model, x, sigmas, extra_args=None, callback=None, disable=None, eta=1., s_noise=1., noise_sampler=None):
|
|
"""Ancestral sampling with DPM-Solver++(2S) second-order steps."""
|
|
extra_args = {} if extra_args is None else extra_args
|
|
noise_sampler = default_noise_sampler(x) if noise_sampler is None else noise_sampler
|
|
s_in = x.new_ones([x.shape[0]])
|
|
sigma_fn = lambda t: t.neg().exp()
|
|
t_fn = lambda sigma: sigma.log().neg()
|
|
|
|
for i in trange(len(sigmas) - 1, disable=disable):
|
|
denoised = model(x, sigmas[i] * s_in, **extra_args)
|
|
sigma_down, sigma_up = get_ancestral_step(sigmas[i], sigmas[i + 1], eta=eta)
|
|
if callback is not None:
|
|
callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigmas[i], 'denoised': denoised})
|
|
if sigma_down == 0:
|
|
# Euler method
|
|
d = to_d(x, sigmas[i], denoised)
|
|
dt = sigma_down - sigmas[i]
|
|
x = x + d * dt
|
|
else:
|
|
# DPM-Solver++(2S)
|
|
t, t_next = t_fn(sigmas[i]), t_fn(sigma_down)
|
|
r = 1 / 2
|
|
h = t_next - t
|
|
s = t + r * h
|
|
x_2 = (sigma_fn(s) / sigma_fn(t)) * x - (-h * r).expm1() * denoised
|
|
denoised_2 = model(x_2, sigma_fn(s) * s_in, **extra_args)
|
|
x = (sigma_fn(t_next) / sigma_fn(t)) * x - (-h).expm1() * denoised_2
|
|
# Noise addition
|
|
if sigmas[i + 1] > 0:
|
|
x = x + noise_sampler(sigmas[i], sigmas[i + 1]) * s_noise * sigma_up
|
|
return x
|
|
|
|
|
|
@torch.no_grad()
|
|
def sample_dpmpp_sde(model, x, sigmas, extra_args=None, callback=None, disable=None, eta=1., s_noise=1., noise_sampler=None, r=1 / 2):
|
|
"""DPM-Solver++ (stochastic)."""
|
|
sigma_min, sigma_max = sigmas[sigmas > 0].min(), sigmas.max()
|
|
seed = extra_args.get("seed", None)
|
|
noise_sampler = BrownianTreeNoiseSampler(x, sigma_min, sigma_max, seed=seed, cpu=True) if noise_sampler is None else noise_sampler
|
|
extra_args = {} if extra_args is None else extra_args
|
|
s_in = x.new_ones([x.shape[0]])
|
|
sigma_fn = lambda t: t.neg().exp()
|
|
t_fn = lambda sigma: sigma.log().neg()
|
|
|
|
for i in trange(len(sigmas) - 1, disable=disable):
|
|
denoised = model(x, sigmas[i] * s_in, **extra_args)
|
|
if callback is not None:
|
|
callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigmas[i], 'denoised': denoised})
|
|
if sigmas[i + 1] == 0:
|
|
# Euler method
|
|
d = to_d(x, sigmas[i], denoised)
|
|
dt = sigmas[i + 1] - sigmas[i]
|
|
x = x + d * dt
|
|
else:
|
|
# DPM-Solver++
|
|
t, t_next = t_fn(sigmas[i]), t_fn(sigmas[i + 1])
|
|
h = t_next - t
|
|
s = t + h * r
|
|
fac = 1 / (2 * r)
|
|
|
|
# Step 1
|
|
sd, su = get_ancestral_step(sigma_fn(t), sigma_fn(s), eta)
|
|
s_ = t_fn(sd)
|
|
x_2 = (sigma_fn(s_) / sigma_fn(t)) * x - (t - s_).expm1() * denoised
|
|
x_2 = x_2 + noise_sampler(sigma_fn(t), sigma_fn(s)) * s_noise * su
|
|
denoised_2 = model(x_2, sigma_fn(s) * s_in, **extra_args)
|
|
|
|
# Step 2
|
|
sd, su = get_ancestral_step(sigma_fn(t), sigma_fn(t_next), eta)
|
|
t_next_ = t_fn(sd)
|
|
denoised_d = (1 - fac) * denoised + fac * denoised_2
|
|
x = (sigma_fn(t_next_) / sigma_fn(t)) * x - (t - t_next_).expm1() * denoised_d
|
|
x = x + noise_sampler(sigma_fn(t), sigma_fn(t_next)) * s_noise * su
|
|
return x
|
|
|
|
|
|
@torch.no_grad()
|
|
def sample_dpmpp_2m(model, x, sigmas, extra_args=None, callback=None, disable=None):
|
|
"""DPM-Solver++(2M)."""
|
|
extra_args = {} if extra_args is None else extra_args
|
|
s_in = x.new_ones([x.shape[0]])
|
|
sigma_fn = lambda t: t.neg().exp()
|
|
t_fn = lambda sigma: sigma.log().neg()
|
|
old_denoised = None
|
|
|
|
for i in trange(len(sigmas) - 1, disable=disable):
|
|
denoised = model(x, sigmas[i] * s_in, **extra_args)
|
|
if callback is not None:
|
|
callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigmas[i], 'denoised': denoised})
|
|
t, t_next = t_fn(sigmas[i]), t_fn(sigmas[i + 1])
|
|
h = t_next - t
|
|
if old_denoised is None or sigmas[i + 1] == 0:
|
|
x = (sigma_fn(t_next) / sigma_fn(t)) * x - (-h).expm1() * denoised
|
|
else:
|
|
h_last = t - t_fn(sigmas[i - 1])
|
|
r = h_last / h
|
|
denoised_d = (1 + 1 / (2 * r)) * denoised - (1 / (2 * r)) * old_denoised
|
|
x = (sigma_fn(t_next) / sigma_fn(t)) * x - (-h).expm1() * denoised_d
|
|
old_denoised = denoised
|
|
return x
|
|
|
|
@torch.no_grad()
|
|
def sample_dpmpp_2m_sde(model, x, sigmas, extra_args=None, callback=None, disable=None, eta=1., s_noise=1., noise_sampler=None, solver_type='midpoint'):
|
|
"""DPM-Solver++(2M) SDE."""
|
|
|
|
if solver_type not in {'heun', 'midpoint'}:
|
|
raise ValueError('solver_type must be \'heun\' or \'midpoint\'')
|
|
|
|
seed = extra_args.get("seed", None)
|
|
sigma_min, sigma_max = sigmas[sigmas > 0].min(), sigmas.max()
|
|
noise_sampler = BrownianTreeNoiseSampler(x, sigma_min, sigma_max, seed=seed, cpu=True) if noise_sampler is None else noise_sampler
|
|
extra_args = {} if extra_args is None else extra_args
|
|
s_in = x.new_ones([x.shape[0]])
|
|
|
|
old_denoised = None
|
|
h_last = None
|
|
h = None
|
|
|
|
for i in trange(len(sigmas) - 1, disable=disable):
|
|
denoised = model(x, sigmas[i] * s_in, **extra_args)
|
|
if callback is not None:
|
|
callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigmas[i], 'denoised': denoised})
|
|
if sigmas[i + 1] == 0:
|
|
# Denoising step
|
|
x = denoised
|
|
else:
|
|
# DPM-Solver++(2M) SDE
|
|
t, s = -sigmas[i].log(), -sigmas[i + 1].log()
|
|
h = s - t
|
|
eta_h = eta * h
|
|
|
|
x = sigmas[i + 1] / sigmas[i] * (-eta_h).exp() * x + (-h - eta_h).expm1().neg() * denoised
|
|
|
|
if old_denoised is not None:
|
|
r = h_last / h
|
|
if solver_type == 'heun':
|
|
x = x + ((-h - eta_h).expm1().neg() / (-h - eta_h) + 1) * (1 / r) * (denoised - old_denoised)
|
|
elif solver_type == 'midpoint':
|
|
x = x + 0.5 * (-h - eta_h).expm1().neg() * (1 / r) * (denoised - old_denoised)
|
|
|
|
if eta:
|
|
x = x + noise_sampler(sigmas[i], sigmas[i + 1]) * sigmas[i + 1] * (-2 * eta_h).expm1().neg().sqrt() * s_noise
|
|
|
|
old_denoised = denoised
|
|
h_last = h
|
|
return x
|
|
|
|
@torch.no_grad()
|
|
def sample_dpmpp_3m_sde(model, x, sigmas, extra_args=None, callback=None, disable=None, eta=1., s_noise=1., noise_sampler=None):
|
|
"""DPM-Solver++(3M) SDE."""
|
|
|
|
seed = extra_args.get("seed", None)
|
|
sigma_min, sigma_max = sigmas[sigmas > 0].min(), sigmas.max()
|
|
noise_sampler = BrownianTreeNoiseSampler(x, sigma_min, sigma_max, seed=seed, cpu=True) if noise_sampler is None else noise_sampler
|
|
extra_args = {} if extra_args is None else extra_args
|
|
s_in = x.new_ones([x.shape[0]])
|
|
|
|
denoised_1, denoised_2 = None, None
|
|
h, h_1, h_2 = None, None, None
|
|
|
|
for i in trange(len(sigmas) - 1, disable=disable):
|
|
denoised = model(x, sigmas[i] * s_in, **extra_args)
|
|
if callback is not None:
|
|
callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigmas[i], 'denoised': denoised})
|
|
if sigmas[i + 1] == 0:
|
|
# Denoising step
|
|
x = denoised
|
|
else:
|
|
t, s = -sigmas[i].log(), -sigmas[i + 1].log()
|
|
h = s - t
|
|
h_eta = h * (eta + 1)
|
|
|
|
x = torch.exp(-h_eta) * x + (-h_eta).expm1().neg() * denoised
|
|
|
|
if h_2 is not None:
|
|
r0 = h_1 / h
|
|
r1 = h_2 / h
|
|
d1_0 = (denoised - denoised_1) / r0
|
|
d1_1 = (denoised_1 - denoised_2) / r1
|
|
d1 = d1_0 + (d1_0 - d1_1) * r0 / (r0 + r1)
|
|
d2 = (d1_0 - d1_1) / (r0 + r1)
|
|
phi_2 = h_eta.neg().expm1() / h_eta + 1
|
|
phi_3 = phi_2 / h_eta - 0.5
|
|
x = x + phi_2 * d1 - phi_3 * d2
|
|
elif h_1 is not None:
|
|
r = h_1 / h
|
|
d = (denoised - denoised_1) / r
|
|
phi_2 = h_eta.neg().expm1() / h_eta + 1
|
|
x = x + phi_2 * d
|
|
|
|
if eta:
|
|
x = x + noise_sampler(sigmas[i], sigmas[i + 1]) * sigmas[i + 1] * (-2 * h * eta).expm1().neg().sqrt() * s_noise
|
|
|
|
denoised_1, denoised_2 = denoised, denoised_1
|
|
h_1, h_2 = h, h_1
|
|
return x
|
|
|
|
@torch.no_grad()
|
|
def sample_dpmpp_3m_sde_gpu(model, x, sigmas, extra_args=None, callback=None, disable=None, eta=1., s_noise=1., noise_sampler=None):
|
|
sigma_min, sigma_max = sigmas[sigmas > 0].min(), sigmas.max()
|
|
noise_sampler = BrownianTreeNoiseSampler(x, sigma_min, sigma_max, seed=extra_args.get("seed", None), cpu=False) if noise_sampler is None else noise_sampler
|
|
return sample_dpmpp_3m_sde(model, x, sigmas, extra_args=extra_args, callback=callback, disable=disable, eta=eta, s_noise=s_noise, noise_sampler=noise_sampler)
|
|
|
|
@torch.no_grad()
|
|
def sample_dpmpp_2m_sde_gpu(model, x, sigmas, extra_args=None, callback=None, disable=None, eta=1., s_noise=1., noise_sampler=None, solver_type='midpoint'):
|
|
sigma_min, sigma_max = sigmas[sigmas > 0].min(), sigmas.max()
|
|
noise_sampler = BrownianTreeNoiseSampler(x, sigma_min, sigma_max, seed=extra_args.get("seed", None), cpu=False) if noise_sampler is None else noise_sampler
|
|
return sample_dpmpp_2m_sde(model, x, sigmas, extra_args=extra_args, callback=callback, disable=disable, eta=eta, s_noise=s_noise, noise_sampler=noise_sampler, solver_type=solver_type)
|
|
|
|
@torch.no_grad()
|
|
def sample_dpmpp_sde_gpu(model, x, sigmas, extra_args=None, callback=None, disable=None, eta=1., s_noise=1., noise_sampler=None, r=1 / 2):
|
|
sigma_min, sigma_max = sigmas[sigmas > 0].min(), sigmas.max()
|
|
noise_sampler = BrownianTreeNoiseSampler(x, sigma_min, sigma_max, seed=extra_args.get("seed", None), cpu=False) if noise_sampler is None else noise_sampler
|
|
return sample_dpmpp_sde(model, x, sigmas, extra_args=extra_args, callback=callback, disable=disable, eta=eta, s_noise=s_noise, noise_sampler=noise_sampler, r=r)
|
|
|
|
|
|
def DDPMSampler_step(x, sigma, sigma_prev, noise, noise_sampler):
|
|
alpha_cumprod = 1 / ((sigma * sigma) + 1)
|
|
alpha_cumprod_prev = 1 / ((sigma_prev * sigma_prev) + 1)
|
|
alpha = (alpha_cumprod / alpha_cumprod_prev)
|
|
|
|
mu = (1.0 / alpha).sqrt() * (x - (1 - alpha) * noise / (1 - alpha_cumprod).sqrt())
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if sigma_prev > 0:
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mu += ((1 - alpha) * (1. - alpha_cumprod_prev) / (1. - alpha_cumprod)).sqrt() * noise_sampler(sigma, sigma_prev)
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return mu
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def generic_step_sampler(model, x, sigmas, extra_args=None, callback=None, disable=None, noise_sampler=None, step_function=None):
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extra_args = {} if extra_args is None else extra_args
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noise_sampler = default_noise_sampler(x) if noise_sampler is None else noise_sampler
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s_in = x.new_ones([x.shape[0]])
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for i in trange(len(sigmas) - 1, disable=disable):
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denoised = model(x, sigmas[i] * s_in, **extra_args)
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if callback is not None:
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callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigmas[i], 'denoised': denoised})
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x = step_function(x / torch.sqrt(1.0 + sigmas[i] ** 2.0), sigmas[i], sigmas[i + 1], (x - denoised) / sigmas[i], noise_sampler)
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if sigmas[i + 1] != 0:
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x *= torch.sqrt(1.0 + sigmas[i + 1] ** 2.0)
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return x
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@torch.no_grad()
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def sample_ddpm(model, x, sigmas, extra_args=None, callback=None, disable=None, noise_sampler=None):
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return generic_step_sampler(model, x, sigmas, extra_args, callback, disable, noise_sampler, DDPMSampler_step)
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