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952 lines
30 KiB
Python
952 lines
30 KiB
Python
import math
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import torch
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from scipy import integrate
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from torch import nn
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from torchdiffeq import odeint
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from tqdm.auto import tqdm, trange
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from imaginairy.log_utils import log_latent
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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=7.0, 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)
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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(
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math.log(sigma_max), math.log(sigma_min), n, device=device
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).exp()
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return append_zero(sigmas)
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def get_sigmas_polyexponential(n, sigma_min, sigma_max, rho=1.0, 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(
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ramp * (math.log(sigma_max) - math.log(sigma_min)) + math.log(sigma_min)
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)
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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) / sigma.to("cpu")).to(x.device)
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def get_ancestral_step(sigma_from, sigma_to, eta=1.0):
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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, 0.0
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sigma_up = min(
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sigma_to,
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eta
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* (sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5,
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)
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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, device="cpu").to(x.device)
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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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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, [], device="cpu").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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self.trees = [
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torchsde.BrownianTree(t0, w0, t1, entropy=s, **kwargs) for s in seed # noqa
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]
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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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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):
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self.transform = transform
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t0, t1 = self.transform(torch.as_tensor(sigma_min)), self.transform(
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torch.as_tensor(sigma_max)
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)
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self.tree = BatchedBrownianTree(x, t0, t1, seed)
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def __call__(self, sigma, sigma_next):
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t0, t1 = self.transform(torch.as_tensor(sigma)), self.transform(
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torch.as_tensor(sigma_next)
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)
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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(
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model,
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x,
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sigmas,
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extra_args=None,
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callback=None,
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disable=None,
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s_churn=0.0,
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s_tmin=0.0,
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s_tmax=float("inf"),
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s_noise=1.0,
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):
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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 = (
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min(s_churn / (len(sigmas) - 1), 2**0.5 - 1)
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if s_tmin <= sigmas[i] <= s_tmax
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else 0.0
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)
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eps = torch.randn_like(x, device="cpu").to(x.device) * s_noise
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sigma_hat = sigmas[i] * (gamma + 1)
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if gamma > 0:
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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(
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{
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"x": x,
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"i": i,
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"sigma": sigmas[i],
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"sigma_hat": sigma_hat,
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"denoised": denoised,
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}
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)
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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(
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model,
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x,
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sigmas,
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extra_args=None,
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callback=None,
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disable=None,
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eta=1.0,
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s_noise=1.0,
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noise_sampler=None,
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):
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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(
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{
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"x": x,
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"i": i,
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"sigma": sigmas[i],
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"sigma_hat": sigmas[i],
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"denoised": denoised,
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}
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)
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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(
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model,
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x,
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sigmas,
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extra_args=None,
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callback=None,
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disable=None,
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s_churn=0.0,
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s_tmin=0.0,
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s_tmax=float("inf"),
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s_noise=1.0,
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):
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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 = (
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min(s_churn / (len(sigmas) - 1), 2**0.5 - 1)
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if s_tmin <= sigmas[i] <= s_tmax
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else 0.0
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)
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eps = torch.randn_like(x, device="cpu").to(x.device) * s_noise
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sigma_hat = sigmas[i] * (gamma + 1)
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if gamma > 0:
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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(
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{
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"x": x,
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"i": i,
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"sigma": sigmas[i],
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"sigma_hat": sigma_hat,
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"denoised": denoised,
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}
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)
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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(
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model,
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x,
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sigmas,
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extra_args=None,
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callback=None,
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disable=None,
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s_churn=0.0,
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s_tmin=0.0,
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s_tmax=float("inf"),
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s_noise=1.0,
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):
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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 = (
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min(s_churn / (len(sigmas) - 1), 2**0.5 - 1)
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if s_tmin <= sigmas[i] <= s_tmax
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else 0.0
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)
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eps = torch.randn_like(x, device="cpu").to(x.device) * s_noise
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sigma_hat = sigmas[i] * (gamma + 1)
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if gamma > 0:
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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(
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{
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"x": x,
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"i": i,
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"sigma": sigmas[i],
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"sigma_hat": sigma_hat,
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"denoised": denoised,
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}
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)
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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(
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model,
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x,
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sigmas,
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extra_args=None,
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callback=None,
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disable=None,
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eta=1.0,
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s_noise=1.0,
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noise_sampler=None,
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):
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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(
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{
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"x": x,
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"i": i,
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"sigma": sigmas[i],
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"sigma_hat": sigmas[i],
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"denoised": denoised,
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}
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)
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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 = 1.0
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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(
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{
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"x": x,
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"i": i,
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"sigma": sigmas[i],
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"sigma_hat": sigmas[i],
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"denoised": denoised,
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}
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)
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cur_order = min(i + 1, order)
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coeffs = [
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linear_multistep_coeff(cur_order, sigmas_cpu, i, j)
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for j in range(cur_order)
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]
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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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@torch.no_grad()
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def log_likelihood(
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model, x, sigma_min, sigma_max, extra_args=None, atol=1e-4, rtol=1e-4
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):
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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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v = torch.randint_like(x, 2, device="cpu") * 2 - 1
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fevals = 0
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def ode_fn(sigma, x):
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nonlocal fevals
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with torch.enable_grad():
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x = x[0].detach().requires_grad_()
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denoised = model(x, sigma * s_in, **extra_args)
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d = to_d(x, sigma, denoised)
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fevals += 1
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grad = torch.autograd.grad((d * v).sum(), x)[0]
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d_ll = (v * grad).flatten(1).sum(1)
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return d.detach(), d_ll
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x_min = x, x.new_zeros([x.shape[0]])
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t = x.new_tensor([sigma_min, sigma_max])
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sol = odeint(ode_fn, x_min, t, atol=atol, rtol=rtol, method="dopri5")
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latent, delta_ll = sol[0][-1], sol[1][-1]
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ll_prior = (
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torch.distributions.Normal(0, sigma_max).log_prob(latent).flatten(1).sum(1)
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)
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return ll_prior + delta_ll, {"fevals": fevals}
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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__(
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self, h, pcoeff, icoeff, dcoeff, order=1, accept_safety=0.81, eps=1e-8
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):
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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
|
|
)
|
|
factor = self.limiter(factor)
|
|
accept = factor >= self.accept_safety
|
|
if accept:
|
|
self.errs[2] = self.errs[1]
|
|
self.errs[1] = self.errs[0]
|
|
self.h *= factor
|
|
return accept
|
|
|
|
|
|
class DPMSolver(nn.Module):
|
|
"""DPM-Solver. See https://arxiv.org/abs/2206.00927."""
|
|
|
|
def __init__(self, model, extra_args=None, eps_callback=None, info_callback=None):
|
|
super().__init__()
|
|
self.model = model
|
|
self.extra_args = {} if extra_args is None else extra_args
|
|
self.eps_callback = eps_callback
|
|
self.info_callback = info_callback
|
|
|
|
def t(self, sigma):
|
|
return -sigma.log()
|
|
|
|
def sigma(self, t):
|
|
return t.to("cpu").neg().exp().to(self.model.device)
|
|
|
|
def eps(self, eps_cache, key, x, t, *args, **kwargs):
|
|
if key in eps_cache:
|
|
return eps_cache[key], eps_cache
|
|
sigma = self.sigma(t) * x.new_ones([x.shape[0]])
|
|
eps = (
|
|
x - self.model(x, sigma, *args, **self.extra_args, **kwargs)
|
|
) / self.sigma(t)
|
|
if self.eps_callback is not None:
|
|
self.eps_callback()
|
|
return eps, {key: eps, **eps_cache}
|
|
|
|
def dpm_solver_1_step(self, x, t, t_next, eps_cache=None):
|
|
eps_cache = {} if eps_cache is None else eps_cache
|
|
h = t_next - t
|
|
eps, eps_cache = self.eps(eps_cache, "eps", x, t)
|
|
x_1 = x - self.sigma(t_next) * h.expm1() * eps
|
|
return x_1, eps_cache
|
|
|
|
def dpm_solver_2_step(self, x, t, t_next, r1=1 / 2, eps_cache=None):
|
|
eps_cache = {} if eps_cache is None else eps_cache
|
|
h = t_next - t
|
|
eps, eps_cache = self.eps(eps_cache, "eps", x, t)
|
|
s1 = t + r1 * h
|
|
u1 = x - self.sigma(s1) * (r1 * h).expm1() * eps
|
|
eps_r1, eps_cache = self.eps(eps_cache, "eps_r1", u1, s1)
|
|
x_2 = (
|
|
x
|
|
- self.sigma(t_next) * h.expm1() * eps
|
|
- self.sigma(t_next) / (2 * r1) * h.expm1() * (eps_r1 - eps)
|
|
)
|
|
return x_2, eps_cache
|
|
|
|
def dpm_solver_3_step(self, x, t, t_next, r1=1 / 3, r2=2 / 3, eps_cache=None):
|
|
eps_cache = {} if eps_cache is None else eps_cache
|
|
h = t_next - t
|
|
eps, eps_cache = self.eps(eps_cache, "eps", x, t)
|
|
s1 = t + r1 * h
|
|
s2 = t + r2 * h
|
|
u1 = x - self.sigma(s1) * (r1 * h).expm1() * eps
|
|
eps_r1, eps_cache = self.eps(eps_cache, "eps_r1", u1, s1)
|
|
u2 = (
|
|
x
|
|
- self.sigma(s2) * (r2 * h).expm1() * eps
|
|
- self.sigma(s2)
|
|
* (r2 / r1)
|
|
* ((r2 * h).expm1() / (r2 * h) - 1)
|
|
* (eps_r1 - eps)
|
|
)
|
|
eps_r2, eps_cache = self.eps(eps_cache, "eps_r2", u2, s2)
|
|
x_3 = (
|
|
x
|
|
- self.sigma(t_next) * h.expm1() * eps
|
|
- self.sigma(t_next) / r2 * (h.expm1() / h - 1) * (eps_r2 - eps)
|
|
)
|
|
return x_3, eps_cache
|
|
|
|
def dpm_solver_fast(
|
|
self, x, t_start, t_end, nfe, eta=0.0, s_noise=1.0, noise_sampler=None
|
|
):
|
|
noise_sampler = (
|
|
default_noise_sampler(x) if noise_sampler is None else noise_sampler
|
|
)
|
|
if not t_end > t_start and eta:
|
|
raise ValueError("eta must be 0 for reverse sampling")
|
|
|
|
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, 0.0
|
|
|
|
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=0.0,
|
|
icoeff=1.0,
|
|
dcoeff=0.0,
|
|
accept_safety=0.81,
|
|
eta=0.0,
|
|
s_noise=1.0,
|
|
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, 0.0
|
|
|
|
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=0.0,
|
|
s_noise=1.0,
|
|
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=0.0,
|
|
icoeff=1.0,
|
|
dcoeff=0.0,
|
|
accept_safety=0.81,
|
|
eta=0.0,
|
|
s_noise=1.0,
|
|
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=1.0,
|
|
s_noise=1.0,
|
|
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]])
|
|
|
|
def sigma_fn(t):
|
|
return t.neg().exp()
|
|
|
|
def t_fn(sigma):
|
|
return sigma.to("cpu").log().neg().to(x.device)
|
|
|
|
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=1.0,
|
|
s_noise=1.0,
|
|
noise_sampler=None,
|
|
r=1 / 2,
|
|
):
|
|
"""DPM-Solver++ (stochastic)."""
|
|
sigma_min, sigma_max = sigmas[sigmas > 0].min(), sigmas.max()
|
|
noise_sampler = (
|
|
BrownianTreeNoiseSampler(x, sigma_min, sigma_max)
|
|
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]])
|
|
|
|
def sigma_fn(t):
|
|
return t.neg().exp()
|
|
|
|
def t_fn(sigma):
|
|
return sigma.to("cpu").log().neg().to(x.device)
|
|
|
|
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]])
|
|
|
|
def sigma_fn(t):
|
|
return t.neg().exp()
|
|
|
|
def t_fn(sigma):
|
|
return sigma.to("cpu").log().neg().to(x.device)
|
|
|
|
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
|
|
log_latent(x, "K_dpmpp_2m_x")
|
|
return x
|