fix: make k-diffusion samplers deterministic
- add test for hashes on mps. images look same on CUDA but are slightly different.pull/1/head
Bryce
2 years ago
parent
b4a3b8c2b3
commit
bb665b9eb6
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import math
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import torch
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from scipy import integrate
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from torchdiffeq import odeint
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from tqdm.auto import tqdm, trange
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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)
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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_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):
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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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sigma_up = (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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@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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eps = torch.randn_like(x) * 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({'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):
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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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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])
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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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x = x + torch.randn_like(x) * 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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eps = torch.randn_like(x) * 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({'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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eps = torch.randn_like(x) * 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({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigma_hat, 'denoised': denoised})
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# Midpoint method, where the midpoint is chosen according to a rho=3 Karras schedule
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sigma_mid = ((sigma_hat ** (1 / 3) + sigmas[i + 1] ** (1 / 3)) / 2) ** 3
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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):
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"""Ancestral sampling with DPM-Solver inspired second-order steps."""
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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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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])
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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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# Midpoint method, where the midpoint is chosen according to a rho=3 Karras schedule
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sigma_mid = ((sigmas[i] ** (1 / 3) + sigma_down ** (1 / 3)) / 2) ** 3
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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 + torch.randn_like(x) * 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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@torch.no_grad()
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def log_likelihood(model, x, sigma_min, sigma_max, extra_args=None, atol=1e-4, rtol=1e-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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v = torch.randint_like(x, 2) * 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 = torch.distributions.Normal(0, sigma_max).log_prob(latent).flatten(1).sum(1)
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return ll_prior + delta_ll, {'fevals': fevals}
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