import math from scipy import integrate import torch from torch import nn from torchdiffeq import odeint import torchsde from tqdm.auto import trange, tqdm from . import utils def append_zero(x): return torch.cat([x, x.new_zeros([1])]) def get_sigmas_karras(n, sigma_min, sigma_max, rho=7., device='cpu'): """Constructs the noise schedule of Karras et al. (2022).""" ramp = torch.linspace(0, 1, n) min_inv_rho = sigma_min ** (1 / rho) max_inv_rho = sigma_max ** (1 / rho) sigmas = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho return append_zero(sigmas).to(device) def get_sigmas_exponential(n, sigma_min, sigma_max, device='cpu'): """Constructs an exponential noise schedule.""" sigmas = torch.linspace(math.log(sigma_max), math.log(sigma_min), n, device=device).exp() return append_zero(sigmas) def get_sigmas_polyexponential(n, sigma_min, sigma_max, rho=1., device='cpu'): """Constructs an polynomial in log sigma noise schedule.""" ramp = torch.linspace(1, 0, n, device=device) ** rho sigmas = torch.exp(ramp * (math.log(sigma_max) - math.log(sigma_min)) + math.log(sigma_min)) return append_zero(sigmas) def get_sigmas_vp(n, beta_d=19.9, beta_min=0.1, eps_s=1e-3, device='cpu'): """Constructs a continuous VP noise schedule.""" t = torch.linspace(1, eps_s, n, device=device) sigmas = torch.sqrt(torch.exp(beta_d * t ** 2 / 2 + beta_min * t) - 1) return append_zero(sigmas) def to_d(x, sigma, denoised): """Converts a denoiser output to a Karras ODE derivative.""" return (x - denoised) / utils.append_dims(sigma, x.ndim) def get_ancestral_step(sigma_from, sigma_to, eta=1.): """Calculates the noise level (sigma_down) to step down to and the amount of noise to add (sigma_up) when doing an ancestral sampling step.""" if not eta: return sigma_to, 0. sigma_up = min(sigma_to, eta * (sigma_to ** 2 * (sigma_from ** 2 - sigma_to ** 2) / sigma_from ** 2) ** 0.5) sigma_down = (sigma_to ** 2 - sigma_up ** 2) ** 0.5 return sigma_down, sigma_up def default_noise_sampler(x): return lambda sigma, sigma_next: torch.randn_like(x) class BatchedBrownianTree: """A wrapper around torchsde.BrownianTree that enables batches of entropy.""" def __init__(self, x, t0, t1, seed=None, **kwargs): t0, t1, self.sign = self.sort(t0, t1) w0 = kwargs.get('w0', torch.zeros_like(x)) if seed is None: seed = torch.randint(0, 2 ** 63 - 1, []).item() self.batched = True try: assert len(seed) == x.shape[0] w0 = w0[0] except TypeError: seed = [seed] self.batched = False self.trees = [torchsde.BrownianTree(t0, w0, t1, entropy=s, **kwargs) for s in seed] @staticmethod def sort(a, b): return (a, b, 1) if a < b else (b, a, -1) def __call__(self, t0, t1): t0, t1, sign = self.sort(t0, t1) w = torch.stack([tree(t0, t1) for tree in self.trees]) * (self.sign * sign) return w if self.batched else w[0] class BrownianTreeNoiseSampler: """A noise sampler backed by a torchsde.BrownianTree. Args: x (Tensor): The tensor whose shape, device and dtype to use to generate random samples. sigma_min (float): The low end of the valid interval. sigma_max (float): The high end of the valid interval. seed (int or List[int]): The random seed. If a list of seeds is supplied instead of a single integer, then the noise sampler will use one BrownianTree per batch item, each with its own seed. transform (callable): A function that maps sigma to the sampler's internal timestep. """ def __init__(self, x, sigma_min, sigma_max, seed=None, transform=lambda x: x): self.transform = transform t0, t1 = self.transform(torch.as_tensor(sigma_min)), self.transform(torch.as_tensor(sigma_max)) self.tree = BatchedBrownianTree(x, t0, t1, seed) def __call__(self, sigma, sigma_next): t0, t1 = self.transform(torch.as_tensor(sigma)), self.transform(torch.as_tensor(sigma_next)) return self.tree(t0, t1) / (t1 - t0).abs().sqrt() @torch.no_grad() 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.): """Implements Algorithm 2 (Euler steps) from Karras et al. (2022).""" extra_args = {} if extra_args is None else extra_args s_in = x.new_ones([x.shape[0]]) for i in trange(len(sigmas) - 1, disable=disable): gamma = min(s_churn / (len(sigmas) - 1), 2 ** 0.5 - 1) if s_tmin <= sigmas[i] <= s_tmax else 0. eps = torch.randn_like(x) * s_noise sigma_hat = sigmas[i] * (gamma + 1) if gamma > 0: x = x + eps * (sigma_hat ** 2 - sigmas[i] ** 2) ** 0.5 denoised = model(x, sigma_hat * s_in, **extra_args) d = to_d(x, sigma_hat, denoised) if callback is not None: callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigma_hat, 'denoised': denoised}) dt = sigmas[i + 1] - sigma_hat # Euler method x = x + d * dt return x @torch.no_grad() def sample_euler_ancestral(model, x, sigmas, extra_args=None, callback=None, disable=None, eta=1., s_noise=1., noise_sampler=None): """Ancestral sampling with Euler method 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]]) 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}) d = to_d(x, sigmas[i], denoised) # Euler method dt = sigma_down - sigmas[i] x = x + d * dt 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_heun(model, x, sigmas, extra_args=None, callback=None, disable=None, s_churn=0., s_tmin=0., s_tmax=float('inf'), s_noise=1.): """Implements Algorithm 2 (Heun steps) from Karras et al. (2022).""" extra_args = {} if extra_args is None else extra_args s_in = x.new_ones([x.shape[0]]) for i in trange(len(sigmas) - 1, disable=disable): gamma = min(s_churn / (len(sigmas) - 1), 2 ** 0.5 - 1) if s_tmin <= sigmas[i] <= s_tmax else 0. eps = torch.randn_like(x) * s_noise sigma_hat = sigmas[i] * (gamma + 1) if gamma > 0: x = x + eps * (sigma_hat ** 2 - sigmas[i] ** 2) ** 0.5 denoised = model(x, sigma_hat * s_in, **extra_args) d = to_d(x, sigma_hat, denoised) if callback is not None: callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigma_hat, 'denoised': denoised}) dt = sigmas[i + 1] - sigma_hat if sigmas[i + 1] == 0: # Euler method x = x + d * dt else: # Heun's method x_2 = x + d * dt denoised_2 = model(x_2, sigmas[i + 1] * s_in, **extra_args) d_2 = to_d(x_2, sigmas[i + 1], denoised_2) d_prime = (d + d_2) / 2 x = x + d_prime * dt return x @torch.no_grad() 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.): """A sampler inspired by DPM-Solver-2 and Algorithm 2 from Karras et al. (2022).""" extra_args = {} if extra_args is None else extra_args s_in = x.new_ones([x.shape[0]]) for i in trange(len(sigmas) - 1, disable=disable): gamma = min(s_churn / (len(sigmas) - 1), 2 ** 0.5 - 1) if s_tmin <= sigmas[i] <= s_tmax else 0. eps = torch.randn_like(x) * s_noise sigma_hat = sigmas[i] * (gamma + 1) if gamma > 0: x = x + eps * (sigma_hat ** 2 - sigmas[i] ** 2) ** 0.5 denoised = model(x, sigma_hat * s_in, **extra_args) d = to_d(x, sigma_hat, denoised) if callback is not None: callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigma_hat, 'denoised': denoised}) if sigmas[i + 1] == 0: # Euler method dt = sigmas[i + 1] - sigma_hat x = x + d * dt else: # DPM-Solver-2 sigma_mid = sigma_hat.log().lerp(sigmas[i + 1].log(), 0.5).exp() dt_1 = sigma_mid - sigma_hat dt_2 = sigmas[i + 1] - sigma_hat x_2 = x + d * dt_1 denoised_2 = model(x_2, sigma_mid * s_in, **extra_args) d_2 = to_d(x_2, sigma_mid, denoised_2) x = x + d_2 * dt_2 return x @torch.no_grad() def sample_dpm_2_ancestral(model, x, sigmas, extra_args=None, callback=None, disable=None, eta=1., s_noise=1., noise_sampler=None): """Ancestral sampling with DPM-Solver 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]]) 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}) d = to_d(x, sigmas[i], denoised) if sigma_down == 0: # Euler method dt = sigma_down - sigmas[i] x = x + d * dt else: # DPM-Solver-2 sigma_mid = sigmas[i].log().lerp(sigma_down.log(), 0.5).exp() dt_1 = sigma_mid - sigmas[i] dt_2 = sigma_down - sigmas[i] x_2 = x + d * dt_1 denoised_2 = model(x_2, sigma_mid * s_in, **extra_args) d_2 = to_d(x_2, sigma_mid, denoised_2) x = x + d_2 * dt_2 x = x + noise_sampler(sigmas[i], sigmas[i + 1]) * s_noise * sigma_up return x def linear_multistep_coeff(order, t, i, j): if order - 1 > i: raise ValueError(f'Order {order} too high for step {i}') def fn(tau): prod = 1. for k in range(order): if j == k: continue prod *= (tau - t[i - k]) / (t[i - j] - t[i - k]) return prod return integrate.quad(fn, t[i], t[i + 1], epsrel=1e-4)[0] @torch.no_grad() def sample_lms(model, x, sigmas, extra_args=None, callback=None, disable=None, order=4): extra_args = {} if extra_args is None else extra_args s_in = x.new_ones([x.shape[0]]) sigmas_cpu = sigmas.detach().cpu().numpy() ds = [] for i in trange(len(sigmas) - 1, disable=disable): denoised = model(x, sigmas[i] * s_in, **extra_args) d = to_d(x, sigmas[i], denoised) ds.append(d) if len(ds) > order: ds.pop(0) if callback is not None: callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigmas[i], 'denoised': denoised}) cur_order = min(i + 1, order) coeffs = [linear_multistep_coeff(cur_order, sigmas_cpu, i, j) for j in range(cur_order)] x = x + sum(coeff * d for coeff, d in zip(coeffs, reversed(ds))) return x @torch.no_grad() def log_likelihood(model, x, sigma_min, sigma_max, extra_args=None, atol=1e-4, rtol=1e-4): extra_args = {} if extra_args is None else extra_args s_in = x.new_ones([x.shape[0]]) v = torch.randint_like(x, 2) * 2 - 1 fevals = 0 def ode_fn(sigma, x): nonlocal fevals with torch.enable_grad(): x = x[0].detach().requires_grad_() denoised = model(x, sigma * s_in, **extra_args) d = to_d(x, sigma, denoised) fevals += 1 grad = torch.autograd.grad((d * v).sum(), x)[0] d_ll = (v * grad).flatten(1).sum(1) return d.detach(), d_ll x_min = x, x.new_zeros([x.shape[0]]) t = x.new_tensor([sigma_min, sigma_max]) sol = odeint(ode_fn, x_min, t, atol=atol, rtol=rtol, method='dopri5') latent, delta_ll = sol[0][-1], sol[1][-1] ll_prior = torch.distributions.Normal(0, sigma_max).log_prob(latent).flatten(1).sum(1) return ll_prior + delta_ll, {'fevals': fevals} class PIDStepSizeController: """A PID controller for ODE adaptive step size control.""" def __init__(self, h, pcoeff, icoeff, dcoeff, order=1, accept_safety=0.81, eps=1e-8): self.h = h self.b1 = (pcoeff + icoeff + dcoeff) / order self.b2 = -(pcoeff + 2 * dcoeff) / order self.b3 = dcoeff / order self.accept_safety = accept_safety self.eps = eps self.errs = [] def limiter(self, x): return 1 + math.atan(x - 1) def propose_step(self, error): inv_error = 1 / (float(error) + self.eps) if not self.errs: self.errs = [inv_error, inv_error, inv_error] self.errs[0] = inv_error 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.neg().exp() 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., s_noise=1., 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. 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() 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]]) 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\'') 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]]) old_denoised = None h_last = 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.""" 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]]) denoised_1, denoised_2 = None, None h_1, h_2 = 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