884 lines
38 KiB
Python
884 lines
38 KiB
Python
#code taken from: https://github.com/wl-zhao/UniPC and modified
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import torch
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import torch.nn.functional as F
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import math
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from tqdm.auto import trange, tqdm
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class NoiseScheduleVP:
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def __init__(
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self,
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schedule='discrete',
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betas=None,
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alphas_cumprod=None,
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continuous_beta_0=0.1,
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continuous_beta_1=20.,
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):
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"""Create a wrapper class for the forward SDE (VP type).
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***
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Update: We support discrete-time diffusion models by implementing a picewise linear interpolation for log_alpha_t.
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We recommend to use schedule='discrete' for the discrete-time diffusion models, especially for high-resolution images.
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***
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The forward SDE ensures that the condition distribution q_{t|0}(x_t | x_0) = N ( alpha_t * x_0, sigma_t^2 * I ).
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We further define lambda_t = log(alpha_t) - log(sigma_t), which is the half-logSNR (described in the DPM-Solver paper).
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Therefore, we implement the functions for computing alpha_t, sigma_t and lambda_t. For t in [0, T], we have:
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log_alpha_t = self.marginal_log_mean_coeff(t)
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sigma_t = self.marginal_std(t)
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lambda_t = self.marginal_lambda(t)
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Moreover, as lambda(t) is an invertible function, we also support its inverse function:
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t = self.inverse_lambda(lambda_t)
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===============================================================
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We support both discrete-time DPMs (trained on n = 0, 1, ..., N-1) and continuous-time DPMs (trained on t in [t_0, T]).
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1. For discrete-time DPMs:
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For discrete-time DPMs trained on n = 0, 1, ..., N-1, we convert the discrete steps to continuous time steps by:
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t_i = (i + 1) / N
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e.g. for N = 1000, we have t_0 = 1e-3 and T = t_{N-1} = 1.
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We solve the corresponding diffusion ODE from time T = 1 to time t_0 = 1e-3.
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Args:
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betas: A `torch.Tensor`. The beta array for the discrete-time DPM. (See the original DDPM paper for details)
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alphas_cumprod: A `torch.Tensor`. The cumprod alphas for the discrete-time DPM. (See the original DDPM paper for details)
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Note that we always have alphas_cumprod = cumprod(betas). Therefore, we only need to set one of `betas` and `alphas_cumprod`.
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**Important**: Please pay special attention for the args for `alphas_cumprod`:
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The `alphas_cumprod` is the \hat{alpha_n} arrays in the notations of DDPM. Specifically, DDPMs assume that
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q_{t_n | 0}(x_{t_n} | x_0) = N ( \sqrt{\hat{alpha_n}} * x_0, (1 - \hat{alpha_n}) * I ).
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Therefore, the notation \hat{alpha_n} is different from the notation alpha_t in DPM-Solver. In fact, we have
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alpha_{t_n} = \sqrt{\hat{alpha_n}},
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and
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log(alpha_{t_n}) = 0.5 * log(\hat{alpha_n}).
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2. For continuous-time DPMs:
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We support two types of VPSDEs: linear (DDPM) and cosine (improved-DDPM). The hyperparameters for the noise
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schedule are the default settings in DDPM and improved-DDPM:
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Args:
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beta_min: A `float` number. The smallest beta for the linear schedule.
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beta_max: A `float` number. The largest beta for the linear schedule.
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cosine_s: A `float` number. The hyperparameter in the cosine schedule.
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cosine_beta_max: A `float` number. The hyperparameter in the cosine schedule.
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T: A `float` number. The ending time of the forward process.
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===============================================================
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Args:
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schedule: A `str`. The noise schedule of the forward SDE. 'discrete' for discrete-time DPMs,
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'linear' or 'cosine' for continuous-time DPMs.
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Returns:
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A wrapper object of the forward SDE (VP type).
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===============================================================
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Example:
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# For discrete-time DPMs, given betas (the beta array for n = 0, 1, ..., N - 1):
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>>> ns = NoiseScheduleVP('discrete', betas=betas)
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# For discrete-time DPMs, given alphas_cumprod (the \hat{alpha_n} array for n = 0, 1, ..., N - 1):
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>>> ns = NoiseScheduleVP('discrete', alphas_cumprod=alphas_cumprod)
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# For continuous-time DPMs (VPSDE), linear schedule:
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>>> ns = NoiseScheduleVP('linear', continuous_beta_0=0.1, continuous_beta_1=20.)
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"""
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if schedule not in ['discrete', 'linear', 'cosine']:
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raise ValueError("Unsupported noise schedule {}. The schedule needs to be 'discrete' or 'linear' or 'cosine'".format(schedule))
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self.schedule = schedule
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if schedule == 'discrete':
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if betas is not None:
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log_alphas = 0.5 * torch.log(1 - betas).cumsum(dim=0)
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else:
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assert alphas_cumprod is not None
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log_alphas = 0.5 * torch.log(alphas_cumprod)
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self.total_N = len(log_alphas)
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self.T = 1.
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self.t_array = torch.linspace(0., 1., self.total_N + 1)[1:].reshape((1, -1))
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self.log_alpha_array = log_alphas.reshape((1, -1,))
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else:
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self.total_N = 1000
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self.beta_0 = continuous_beta_0
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self.beta_1 = continuous_beta_1
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self.cosine_s = 0.008
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self.cosine_beta_max = 999.
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self.cosine_t_max = math.atan(self.cosine_beta_max * (1. + self.cosine_s) / math.pi) * 2. * (1. + self.cosine_s) / math.pi - self.cosine_s
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self.cosine_log_alpha_0 = math.log(math.cos(self.cosine_s / (1. + self.cosine_s) * math.pi / 2.))
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self.schedule = schedule
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if schedule == 'cosine':
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# For the cosine schedule, T = 1 will have numerical issues. So we manually set the ending time T.
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# Note that T = 0.9946 may be not the optimal setting. However, we find it works well.
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self.T = 0.9946
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else:
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self.T = 1.
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def marginal_log_mean_coeff(self, t):
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"""
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Compute log(alpha_t) of a given continuous-time label t in [0, T].
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"""
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if self.schedule == 'discrete':
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return interpolate_fn(t.reshape((-1, 1)), self.t_array.to(t.device), self.log_alpha_array.to(t.device)).reshape((-1))
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elif self.schedule == 'linear':
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return -0.25 * t ** 2 * (self.beta_1 - self.beta_0) - 0.5 * t * self.beta_0
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elif self.schedule == 'cosine':
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log_alpha_fn = lambda s: torch.log(torch.cos((s + self.cosine_s) / (1. + self.cosine_s) * math.pi / 2.))
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log_alpha_t = log_alpha_fn(t) - self.cosine_log_alpha_0
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return log_alpha_t
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def marginal_alpha(self, t):
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"""
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Compute alpha_t of a given continuous-time label t in [0, T].
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"""
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return torch.exp(self.marginal_log_mean_coeff(t))
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def marginal_std(self, t):
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"""
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Compute sigma_t of a given continuous-time label t in [0, T].
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"""
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return torch.sqrt(1. - torch.exp(2. * self.marginal_log_mean_coeff(t)))
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def marginal_lambda(self, t):
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"""
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Compute lambda_t = log(alpha_t) - log(sigma_t) of a given continuous-time label t in [0, T].
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"""
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log_mean_coeff = self.marginal_log_mean_coeff(t)
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log_std = 0.5 * torch.log(1. - torch.exp(2. * log_mean_coeff))
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return log_mean_coeff - log_std
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def inverse_lambda(self, lamb):
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"""
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Compute the continuous-time label t in [0, T] of a given half-logSNR lambda_t.
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"""
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if self.schedule == 'linear':
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tmp = 2. * (self.beta_1 - self.beta_0) * torch.logaddexp(-2. * lamb, torch.zeros((1,)).to(lamb))
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Delta = self.beta_0**2 + tmp
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return tmp / (torch.sqrt(Delta) + self.beta_0) / (self.beta_1 - self.beta_0)
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elif self.schedule == 'discrete':
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log_alpha = -0.5 * torch.logaddexp(torch.zeros((1,)).to(lamb.device), -2. * lamb)
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t = interpolate_fn(log_alpha.reshape((-1, 1)), torch.flip(self.log_alpha_array.to(lamb.device), [1]), torch.flip(self.t_array.to(lamb.device), [1]))
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return t.reshape((-1,))
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else:
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log_alpha = -0.5 * torch.logaddexp(-2. * lamb, torch.zeros((1,)).to(lamb))
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t_fn = lambda log_alpha_t: torch.arccos(torch.exp(log_alpha_t + self.cosine_log_alpha_0)) * 2. * (1. + self.cosine_s) / math.pi - self.cosine_s
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t = t_fn(log_alpha)
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return t
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def model_wrapper(
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model,
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sampling_function,
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noise_schedule,
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model_type="noise",
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model_kwargs={},
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guidance_type="uncond",
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condition=None,
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unconditional_condition=None,
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guidance_scale=1.,
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classifier_fn=None,
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classifier_kwargs={},
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):
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"""Create a wrapper function for the noise prediction model.
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DPM-Solver needs to solve the continuous-time diffusion ODEs. For DPMs trained on discrete-time labels, we need to
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firstly wrap the model function to a noise prediction model that accepts the continuous time as the input.
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We support four types of the diffusion model by setting `model_type`:
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1. "noise": noise prediction model. (Trained by predicting noise).
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2. "x_start": data prediction model. (Trained by predicting the data x_0 at time 0).
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3. "v": velocity prediction model. (Trained by predicting the velocity).
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The "v" prediction is derivation detailed in Appendix D of [1], and is used in Imagen-Video [2].
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[1] Salimans, Tim, and Jonathan Ho. "Progressive distillation for fast sampling of diffusion models."
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arXiv preprint arXiv:2202.00512 (2022).
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[2] Ho, Jonathan, et al. "Imagen Video: High Definition Video Generation with Diffusion Models."
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arXiv preprint arXiv:2210.02303 (2022).
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4. "score": marginal score function. (Trained by denoising score matching).
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Note that the score function and the noise prediction model follows a simple relationship:
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```
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noise(x_t, t) = -sigma_t * score(x_t, t)
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```
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We support three types of guided sampling by DPMs by setting `guidance_type`:
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1. "uncond": unconditional sampling by DPMs.
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The input `model` has the following format:
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``
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model(x, t_input, **model_kwargs) -> noise | x_start | v | score
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``
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2. "classifier": classifier guidance sampling [3] by DPMs and another classifier.
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The input `model` has the following format:
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``
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model(x, t_input, **model_kwargs) -> noise | x_start | v | score
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``
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The input `classifier_fn` has the following format:
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``
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classifier_fn(x, t_input, cond, **classifier_kwargs) -> logits(x, t_input, cond)
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``
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[3] P. Dhariwal and A. Q. Nichol, "Diffusion models beat GANs on image synthesis,"
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in Advances in Neural Information Processing Systems, vol. 34, 2021, pp. 8780-8794.
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3. "classifier-free": classifier-free guidance sampling by conditional DPMs.
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The input `model` has the following format:
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``
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model(x, t_input, cond, **model_kwargs) -> noise | x_start | v | score
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``
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And if cond == `unconditional_condition`, the model output is the unconditional DPM output.
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[4] Ho, Jonathan, and Tim Salimans. "Classifier-free diffusion guidance."
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arXiv preprint arXiv:2207.12598 (2022).
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The `t_input` is the time label of the model, which may be discrete-time labels (i.e. 0 to 999)
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or continuous-time labels (i.e. epsilon to T).
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We wrap the model function to accept only `x` and `t_continuous` as inputs, and outputs the predicted noise:
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``
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def model_fn(x, t_continuous) -> noise:
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t_input = get_model_input_time(t_continuous)
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return noise_pred(model, x, t_input, **model_kwargs)
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``
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where `t_continuous` is the continuous time labels (i.e. epsilon to T). And we use `model_fn` for DPM-Solver.
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===============================================================
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Args:
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model: A diffusion model with the corresponding format described above.
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noise_schedule: A noise schedule object, such as NoiseScheduleVP.
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model_type: A `str`. The parameterization type of the diffusion model.
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"noise" or "x_start" or "v" or "score".
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model_kwargs: A `dict`. A dict for the other inputs of the model function.
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guidance_type: A `str`. The type of the guidance for sampling.
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"uncond" or "classifier" or "classifier-free".
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condition: A pytorch tensor. The condition for the guided sampling.
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Only used for "classifier" or "classifier-free" guidance type.
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unconditional_condition: A pytorch tensor. The condition for the unconditional sampling.
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Only used for "classifier-free" guidance type.
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guidance_scale: A `float`. The scale for the guided sampling.
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classifier_fn: A classifier function. Only used for the classifier guidance.
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classifier_kwargs: A `dict`. A dict for the other inputs of the classifier function.
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Returns:
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A noise prediction model that accepts the noised data and the continuous time as the inputs.
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"""
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def get_model_input_time(t_continuous):
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"""
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Convert the continuous-time `t_continuous` (in [epsilon, T]) to the model input time.
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For discrete-time DPMs, we convert `t_continuous` in [1 / N, 1] to `t_input` in [0, 1000 * (N - 1) / N].
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For continuous-time DPMs, we just use `t_continuous`.
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"""
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if noise_schedule.schedule == 'discrete':
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return (t_continuous - 1. / noise_schedule.total_N) * 1000.
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else:
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return t_continuous
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def noise_pred_fn(x, t_continuous, cond=None):
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if t_continuous.reshape((-1,)).shape[0] == 1:
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t_continuous = t_continuous.expand((x.shape[0]))
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t_input = get_model_input_time(t_continuous)
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output = sampling_function(model, x, t_input, **model_kwargs)
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if model_type == "noise":
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return output
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elif model_type == "x_start":
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alpha_t, sigma_t = noise_schedule.marginal_alpha(t_continuous), noise_schedule.marginal_std(t_continuous)
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dims = x.dim()
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return (x - expand_dims(alpha_t, dims) * output) / expand_dims(sigma_t, dims)
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elif model_type == "v":
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alpha_t, sigma_t = noise_schedule.marginal_alpha(t_continuous), noise_schedule.marginal_std(t_continuous)
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dims = x.dim()
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return expand_dims(alpha_t, dims) * output + expand_dims(sigma_t, dims) * x
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elif model_type == "score":
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sigma_t = noise_schedule.marginal_std(t_continuous)
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dims = x.dim()
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return -expand_dims(sigma_t, dims) * output
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def cond_grad_fn(x, t_input):
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"""
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Compute the gradient of the classifier, i.e. nabla_{x} log p_t(cond | x_t).
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"""
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with torch.enable_grad():
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x_in = x.detach().requires_grad_(True)
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log_prob = classifier_fn(x_in, t_input, condition, **classifier_kwargs)
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return torch.autograd.grad(log_prob.sum(), x_in)[0]
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def model_fn(x, t_continuous):
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"""
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The noise predicition model function that is used for DPM-Solver.
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"""
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if t_continuous.reshape((-1,)).shape[0] == 1:
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t_continuous = t_continuous.expand((x.shape[0]))
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if guidance_type == "uncond":
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return noise_pred_fn(x, t_continuous)
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elif guidance_type == "classifier":
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assert classifier_fn is not None
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t_input = get_model_input_time(t_continuous)
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cond_grad = cond_grad_fn(x, t_input)
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sigma_t = noise_schedule.marginal_std(t_continuous)
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noise = noise_pred_fn(x, t_continuous)
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return noise - guidance_scale * expand_dims(sigma_t, dims=cond_grad.dim()) * cond_grad
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elif guidance_type == "classifier-free":
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if guidance_scale == 1. or unconditional_condition is None:
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return noise_pred_fn(x, t_continuous, cond=condition)
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else:
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x_in = torch.cat([x] * 2)
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t_in = torch.cat([t_continuous] * 2)
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c_in = torch.cat([unconditional_condition, condition])
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noise_uncond, noise = noise_pred_fn(x_in, t_in, cond=c_in).chunk(2)
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return noise_uncond + guidance_scale * (noise - noise_uncond)
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assert model_type in ["noise", "x_start", "v"]
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assert guidance_type in ["uncond", "classifier", "classifier-free"]
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return model_fn
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class UniPC:
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def __init__(
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self,
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model_fn,
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noise_schedule,
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predict_x0=True,
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thresholding=False,
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max_val=1.,
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variant='bh1',
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noise_mask=None,
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masked_image=None,
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noise=None,
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):
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"""Construct a UniPC.
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We support both data_prediction and noise_prediction.
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"""
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self.model = model_fn
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self.noise_schedule = noise_schedule
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self.variant = variant
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self.predict_x0 = predict_x0
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self.thresholding = thresholding
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self.max_val = max_val
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self.noise_mask = noise_mask
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self.masked_image = masked_image
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self.noise = noise
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def dynamic_thresholding_fn(self, x0, t=None):
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"""
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The dynamic thresholding method.
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"""
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dims = x0.dim()
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p = self.dynamic_thresholding_ratio
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s = torch.quantile(torch.abs(x0).reshape((x0.shape[0], -1)), p, dim=1)
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s = expand_dims(torch.maximum(s, self.thresholding_max_val * torch.ones_like(s).to(s.device)), dims)
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x0 = torch.clamp(x0, -s, s) / s
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return x0
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def noise_prediction_fn(self, x, t):
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"""
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Return the noise prediction model.
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"""
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if self.noise_mask is not None:
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return self.model(x, t) * self.noise_mask
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else:
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return self.model(x, t)
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def data_prediction_fn(self, x, t):
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"""
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Return the data prediction model (with thresholding).
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"""
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noise = self.noise_prediction_fn(x, t)
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dims = x.dim()
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alpha_t, sigma_t = self.noise_schedule.marginal_alpha(t), self.noise_schedule.marginal_std(t)
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x0 = (x - expand_dims(sigma_t, dims) * noise) / expand_dims(alpha_t, dims)
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if self.thresholding:
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p = 0.995 # A hyperparameter in the paper of "Imagen" [1].
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s = torch.quantile(torch.abs(x0).reshape((x0.shape[0], -1)), p, dim=1)
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s = expand_dims(torch.maximum(s, self.max_val * torch.ones_like(s).to(s.device)), dims)
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x0 = torch.clamp(x0, -s, s) / s
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|
if self.noise_mask is not None:
|
|
x0 = x0 * self.noise_mask + (1. - self.noise_mask) * self.masked_image
|
|
return x0
|
|
|
|
def model_fn(self, x, t):
|
|
"""
|
|
Convert the model to the noise prediction model or the data prediction model.
|
|
"""
|
|
if self.predict_x0:
|
|
return self.data_prediction_fn(x, t)
|
|
else:
|
|
return self.noise_prediction_fn(x, t)
|
|
|
|
def get_time_steps(self, skip_type, t_T, t_0, N, device):
|
|
"""Compute the intermediate time steps for sampling.
|
|
"""
|
|
if skip_type == 'logSNR':
|
|
lambda_T = self.noise_schedule.marginal_lambda(torch.tensor(t_T).to(device))
|
|
lambda_0 = self.noise_schedule.marginal_lambda(torch.tensor(t_0).to(device))
|
|
logSNR_steps = torch.linspace(lambda_T.cpu().item(), lambda_0.cpu().item(), N + 1).to(device)
|
|
return self.noise_schedule.inverse_lambda(logSNR_steps)
|
|
elif skip_type == 'time_uniform':
|
|
return torch.linspace(t_T, t_0, N + 1).to(device)
|
|
elif skip_type == 'time_quadratic':
|
|
t_order = 2
|
|
t = torch.linspace(t_T**(1. / t_order), t_0**(1. / t_order), N + 1).pow(t_order).to(device)
|
|
return t
|
|
else:
|
|
raise ValueError("Unsupported skip_type {}, need to be 'logSNR' or 'time_uniform' or 'time_quadratic'".format(skip_type))
|
|
|
|
def get_orders_and_timesteps_for_singlestep_solver(self, steps, order, skip_type, t_T, t_0, device):
|
|
"""
|
|
Get the order of each step for sampling by the singlestep DPM-Solver.
|
|
"""
|
|
if order == 3:
|
|
K = steps // 3 + 1
|
|
if steps % 3 == 0:
|
|
orders = [3,] * (K - 2) + [2, 1]
|
|
elif steps % 3 == 1:
|
|
orders = [3,] * (K - 1) + [1]
|
|
else:
|
|
orders = [3,] * (K - 1) + [2]
|
|
elif order == 2:
|
|
if steps % 2 == 0:
|
|
K = steps // 2
|
|
orders = [2,] * K
|
|
else:
|
|
K = steps // 2 + 1
|
|
orders = [2,] * (K - 1) + [1]
|
|
elif order == 1:
|
|
K = steps
|
|
orders = [1,] * steps
|
|
else:
|
|
raise ValueError("'order' must be '1' or '2' or '3'.")
|
|
if skip_type == 'logSNR':
|
|
# To reproduce the results in DPM-Solver paper
|
|
timesteps_outer = self.get_time_steps(skip_type, t_T, t_0, K, device)
|
|
else:
|
|
timesteps_outer = self.get_time_steps(skip_type, t_T, t_0, steps, device)[torch.cumsum(torch.tensor([0,] + orders), 0).to(device)]
|
|
return timesteps_outer, orders
|
|
|
|
def denoise_to_zero_fn(self, x, s):
|
|
"""
|
|
Denoise at the final step, which is equivalent to solve the ODE from lambda_s to infty by first-order discretization.
|
|
"""
|
|
return self.data_prediction_fn(x, s)
|
|
|
|
def multistep_uni_pc_update(self, x, model_prev_list, t_prev_list, t, order, **kwargs):
|
|
if len(t.shape) == 0:
|
|
t = t.view(-1)
|
|
if 'bh' in self.variant:
|
|
return self.multistep_uni_pc_bh_update(x, model_prev_list, t_prev_list, t, order, **kwargs)
|
|
else:
|
|
assert self.variant == 'vary_coeff'
|
|
return self.multistep_uni_pc_vary_update(x, model_prev_list, t_prev_list, t, order, **kwargs)
|
|
|
|
def multistep_uni_pc_vary_update(self, x, model_prev_list, t_prev_list, t, order, use_corrector=True):
|
|
print(f'using unified predictor-corrector with order {order} (solver type: vary coeff)')
|
|
ns = self.noise_schedule
|
|
assert order <= len(model_prev_list)
|
|
|
|
# first compute rks
|
|
t_prev_0 = t_prev_list[-1]
|
|
lambda_prev_0 = ns.marginal_lambda(t_prev_0)
|
|
lambda_t = ns.marginal_lambda(t)
|
|
model_prev_0 = model_prev_list[-1]
|
|
sigma_prev_0, sigma_t = ns.marginal_std(t_prev_0), ns.marginal_std(t)
|
|
log_alpha_t = ns.marginal_log_mean_coeff(t)
|
|
alpha_t = torch.exp(log_alpha_t)
|
|
|
|
h = lambda_t - lambda_prev_0
|
|
|
|
rks = []
|
|
D1s = []
|
|
for i in range(1, order):
|
|
t_prev_i = t_prev_list[-(i + 1)]
|
|
model_prev_i = model_prev_list[-(i + 1)]
|
|
lambda_prev_i = ns.marginal_lambda(t_prev_i)
|
|
rk = (lambda_prev_i - lambda_prev_0) / h
|
|
rks.append(rk)
|
|
D1s.append((model_prev_i - model_prev_0) / rk)
|
|
|
|
rks.append(1.)
|
|
rks = torch.tensor(rks, device=x.device)
|
|
|
|
K = len(rks)
|
|
# build C matrix
|
|
C = []
|
|
|
|
col = torch.ones_like(rks)
|
|
for k in range(1, K + 1):
|
|
C.append(col)
|
|
col = col * rks / (k + 1)
|
|
C = torch.stack(C, dim=1)
|
|
|
|
if len(D1s) > 0:
|
|
D1s = torch.stack(D1s, dim=1) # (B, K)
|
|
C_inv_p = torch.linalg.inv(C[:-1, :-1])
|
|
A_p = C_inv_p
|
|
|
|
if use_corrector:
|
|
print('using corrector')
|
|
C_inv = torch.linalg.inv(C)
|
|
A_c = C_inv
|
|
|
|
hh = -h if self.predict_x0 else h
|
|
h_phi_1 = torch.expm1(hh)
|
|
h_phi_ks = []
|
|
factorial_k = 1
|
|
h_phi_k = h_phi_1
|
|
for k in range(1, K + 2):
|
|
h_phi_ks.append(h_phi_k)
|
|
h_phi_k = h_phi_k / hh - 1 / factorial_k
|
|
factorial_k *= (k + 1)
|
|
|
|
model_t = None
|
|
if self.predict_x0:
|
|
x_t_ = (
|
|
sigma_t / sigma_prev_0 * x
|
|
- alpha_t * h_phi_1 * model_prev_0
|
|
)
|
|
# now predictor
|
|
x_t = x_t_
|
|
if len(D1s) > 0:
|
|
# compute the residuals for predictor
|
|
for k in range(K - 1):
|
|
x_t = x_t - alpha_t * h_phi_ks[k + 1] * torch.einsum('bkchw,k->bchw', D1s, A_p[k])
|
|
# now corrector
|
|
if use_corrector:
|
|
model_t = self.model_fn(x_t, t)
|
|
D1_t = (model_t - model_prev_0)
|
|
x_t = x_t_
|
|
k = 0
|
|
for k in range(K - 1):
|
|
x_t = x_t - alpha_t * h_phi_ks[k + 1] * torch.einsum('bkchw,k->bchw', D1s, A_c[k][:-1])
|
|
x_t = x_t - alpha_t * h_phi_ks[K] * (D1_t * A_c[k][-1])
|
|
else:
|
|
log_alpha_prev_0, log_alpha_t = ns.marginal_log_mean_coeff(t_prev_0), ns.marginal_log_mean_coeff(t)
|
|
x_t_ = (
|
|
(torch.exp(log_alpha_t - log_alpha_prev_0)) * x
|
|
- (sigma_t * h_phi_1) * model_prev_0
|
|
)
|
|
# now predictor
|
|
x_t = x_t_
|
|
if len(D1s) > 0:
|
|
# compute the residuals for predictor
|
|
for k in range(K - 1):
|
|
x_t = x_t - sigma_t * h_phi_ks[k + 1] * torch.einsum('bkchw,k->bchw', D1s, A_p[k])
|
|
# now corrector
|
|
if use_corrector:
|
|
model_t = self.model_fn(x_t, t)
|
|
D1_t = (model_t - model_prev_0)
|
|
x_t = x_t_
|
|
k = 0
|
|
for k in range(K - 1):
|
|
x_t = x_t - sigma_t * h_phi_ks[k + 1] * torch.einsum('bkchw,k->bchw', D1s, A_c[k][:-1])
|
|
x_t = x_t - sigma_t * h_phi_ks[K] * (D1_t * A_c[k][-1])
|
|
return x_t, model_t
|
|
|
|
def multistep_uni_pc_bh_update(self, x, model_prev_list, t_prev_list, t, order, x_t=None, use_corrector=True):
|
|
# print(f'using unified predictor-corrector with order {order} (solver type: B(h))')
|
|
ns = self.noise_schedule
|
|
assert order <= len(model_prev_list)
|
|
dims = x.dim()
|
|
|
|
# first compute rks
|
|
t_prev_0 = t_prev_list[-1]
|
|
lambda_prev_0 = ns.marginal_lambda(t_prev_0)
|
|
lambda_t = ns.marginal_lambda(t)
|
|
model_prev_0 = model_prev_list[-1]
|
|
sigma_prev_0, sigma_t = ns.marginal_std(t_prev_0), ns.marginal_std(t)
|
|
log_alpha_prev_0, log_alpha_t = ns.marginal_log_mean_coeff(t_prev_0), ns.marginal_log_mean_coeff(t)
|
|
alpha_t = torch.exp(log_alpha_t)
|
|
|
|
h = lambda_t - lambda_prev_0
|
|
|
|
rks = []
|
|
D1s = []
|
|
for i in range(1, order):
|
|
t_prev_i = t_prev_list[-(i + 1)]
|
|
model_prev_i = model_prev_list[-(i + 1)]
|
|
lambda_prev_i = ns.marginal_lambda(t_prev_i)
|
|
rk = ((lambda_prev_i - lambda_prev_0) / h)[0]
|
|
rks.append(rk)
|
|
D1s.append((model_prev_i - model_prev_0) / rk)
|
|
|
|
rks.append(1.)
|
|
rks = torch.tensor(rks, device=x.device)
|
|
|
|
R = []
|
|
b = []
|
|
|
|
hh = -h[0] if self.predict_x0 else h[0]
|
|
h_phi_1 = torch.expm1(hh) # h\phi_1(h) = e^h - 1
|
|
h_phi_k = h_phi_1 / hh - 1
|
|
|
|
factorial_i = 1
|
|
|
|
if self.variant == 'bh1':
|
|
B_h = hh
|
|
elif self.variant == 'bh2':
|
|
B_h = torch.expm1(hh)
|
|
else:
|
|
raise NotImplementedError()
|
|
|
|
for i in range(1, order + 1):
|
|
R.append(torch.pow(rks, i - 1))
|
|
b.append(h_phi_k * factorial_i / B_h)
|
|
factorial_i *= (i + 1)
|
|
h_phi_k = h_phi_k / hh - 1 / factorial_i
|
|
|
|
R = torch.stack(R)
|
|
b = torch.tensor(b, device=x.device)
|
|
|
|
# now predictor
|
|
use_predictor = len(D1s) > 0 and x_t is None
|
|
if len(D1s) > 0:
|
|
D1s = torch.stack(D1s, dim=1) # (B, K)
|
|
if x_t is None:
|
|
# for order 2, we use a simplified version
|
|
if order == 2:
|
|
rhos_p = torch.tensor([0.5], device=b.device)
|
|
else:
|
|
rhos_p = torch.linalg.solve(R[:-1, :-1], b[:-1])
|
|
else:
|
|
D1s = None
|
|
|
|
if use_corrector:
|
|
# print('using corrector')
|
|
# for order 1, we use a simplified version
|
|
if order == 1:
|
|
rhos_c = torch.tensor([0.5], device=b.device)
|
|
else:
|
|
rhos_c = torch.linalg.solve(R, b)
|
|
|
|
model_t = None
|
|
if self.predict_x0:
|
|
x_t_ = (
|
|
expand_dims(sigma_t / sigma_prev_0, dims) * x
|
|
- expand_dims(alpha_t * h_phi_1, dims)* model_prev_0
|
|
)
|
|
|
|
if x_t is None:
|
|
if use_predictor:
|
|
pred_res = torch.einsum('k,bkchw->bchw', rhos_p, D1s)
|
|
else:
|
|
pred_res = 0
|
|
x_t = x_t_ - expand_dims(alpha_t * B_h, dims) * pred_res
|
|
|
|
if use_corrector:
|
|
model_t = self.model_fn(x_t, t)
|
|
if D1s is not None:
|
|
corr_res = torch.einsum('k,bkchw->bchw', rhos_c[:-1], D1s)
|
|
else:
|
|
corr_res = 0
|
|
D1_t = (model_t - model_prev_0)
|
|
x_t = x_t_ - expand_dims(alpha_t * B_h, dims) * (corr_res + rhos_c[-1] * D1_t)
|
|
else:
|
|
x_t_ = (
|
|
expand_dims(torch.exp(log_alpha_t - log_alpha_prev_0), dimss) * x
|
|
- expand_dims(sigma_t * h_phi_1, dims) * model_prev_0
|
|
)
|
|
if x_t is None:
|
|
if use_predictor:
|
|
pred_res = torch.einsum('k,bkchw->bchw', rhos_p, D1s)
|
|
else:
|
|
pred_res = 0
|
|
x_t = x_t_ - expand_dims(sigma_t * B_h, dims) * pred_res
|
|
|
|
if use_corrector:
|
|
model_t = self.model_fn(x_t, t)
|
|
if D1s is not None:
|
|
corr_res = torch.einsum('k,bkchw->bchw', rhos_c[:-1], D1s)
|
|
else:
|
|
corr_res = 0
|
|
D1_t = (model_t - model_prev_0)
|
|
x_t = x_t_ - expand_dims(sigma_t * B_h, dims) * (corr_res + rhos_c[-1] * D1_t)
|
|
return x_t, model_t
|
|
|
|
|
|
def sample(self, x, timesteps, t_start=None, t_end=None, order=3, skip_type='time_uniform',
|
|
method='singlestep', lower_order_final=True, denoise_to_zero=False, solver_type='dpm_solver',
|
|
atol=0.0078, rtol=0.05, corrector=False,
|
|
):
|
|
t_0 = 1. / self.noise_schedule.total_N if t_end is None else t_end
|
|
t_T = self.noise_schedule.T if t_start is None else t_start
|
|
device = x.device
|
|
steps = len(timesteps) - 1
|
|
if method == 'multistep':
|
|
assert steps >= order
|
|
# timesteps = self.get_time_steps(skip_type=skip_type, t_T=t_T, t_0=t_0, N=steps, device=device)
|
|
assert timesteps.shape[0] - 1 == steps
|
|
# with torch.no_grad():
|
|
for step_index in trange(steps):
|
|
if self.noise_mask is not None:
|
|
x = x * self.noise_mask + (1. - self.noise_mask) * (self.masked_image * self.noise_schedule.marginal_alpha(timesteps[step_index]) + self.noise * self.noise_schedule.marginal_std(timesteps[step_index]))
|
|
if step_index == 0:
|
|
vec_t = timesteps[0].expand((x.shape[0]))
|
|
model_prev_list = [self.model_fn(x, vec_t)]
|
|
t_prev_list = [vec_t]
|
|
elif step_index < order:
|
|
init_order = step_index
|
|
# Init the first `order` values by lower order multistep DPM-Solver.
|
|
# for init_order in range(1, order):
|
|
vec_t = timesteps[init_order].expand(x.shape[0])
|
|
x, model_x = self.multistep_uni_pc_update(x, model_prev_list, t_prev_list, vec_t, init_order, use_corrector=True)
|
|
if model_x is None:
|
|
model_x = self.model_fn(x, vec_t)
|
|
model_prev_list.append(model_x)
|
|
t_prev_list.append(vec_t)
|
|
else:
|
|
extra_final_step = 0
|
|
if step_index == (steps - 1):
|
|
extra_final_step = 1
|
|
for step in range(step_index, step_index + 1 + extra_final_step):
|
|
vec_t = timesteps[step].expand(x.shape[0])
|
|
if lower_order_final:
|
|
step_order = min(order, steps + 1 - step)
|
|
else:
|
|
step_order = order
|
|
# print('this step order:', step_order)
|
|
if step == steps:
|
|
# print('do not run corrector at the last step')
|
|
use_corrector = False
|
|
else:
|
|
use_corrector = True
|
|
x, model_x = self.multistep_uni_pc_update(x, model_prev_list, t_prev_list, vec_t, step_order, use_corrector=use_corrector)
|
|
for i in range(order - 1):
|
|
t_prev_list[i] = t_prev_list[i + 1]
|
|
model_prev_list[i] = model_prev_list[i + 1]
|
|
t_prev_list[-1] = vec_t
|
|
# We do not need to evaluate the final model value.
|
|
if step < steps:
|
|
if model_x is None:
|
|
model_x = self.model_fn(x, vec_t)
|
|
model_prev_list[-1] = model_x
|
|
else:
|
|
raise NotImplementedError()
|
|
if denoise_to_zero:
|
|
x = self.denoise_to_zero_fn(x, torch.ones((x.shape[0],)).to(device) * t_0)
|
|
return x
|
|
|
|
|
|
#############################################################
|
|
# other utility functions
|
|
#############################################################
|
|
|
|
def interpolate_fn(x, xp, yp):
|
|
"""
|
|
A piecewise linear function y = f(x), using xp and yp as keypoints.
|
|
We implement f(x) in a differentiable way (i.e. applicable for autograd).
|
|
The function f(x) is well-defined for all x-axis. (For x beyond the bounds of xp, we use the outmost points of xp to define the linear function.)
|
|
|
|
Args:
|
|
x: PyTorch tensor with shape [N, C], where N is the batch size, C is the number of channels (we use C = 1 for DPM-Solver).
|
|
xp: PyTorch tensor with shape [C, K], where K is the number of keypoints.
|
|
yp: PyTorch tensor with shape [C, K].
|
|
Returns:
|
|
The function values f(x), with shape [N, C].
|
|
"""
|
|
N, K = x.shape[0], xp.shape[1]
|
|
all_x = torch.cat([x.unsqueeze(2), xp.unsqueeze(0).repeat((N, 1, 1))], dim=2)
|
|
sorted_all_x, x_indices = torch.sort(all_x, dim=2)
|
|
x_idx = torch.argmin(x_indices, dim=2)
|
|
cand_start_idx = x_idx - 1
|
|
start_idx = torch.where(
|
|
torch.eq(x_idx, 0),
|
|
torch.tensor(1, device=x.device),
|
|
torch.where(
|
|
torch.eq(x_idx, K), torch.tensor(K - 2, device=x.device), cand_start_idx,
|
|
),
|
|
)
|
|
end_idx = torch.where(torch.eq(start_idx, cand_start_idx), start_idx + 2, start_idx + 1)
|
|
start_x = torch.gather(sorted_all_x, dim=2, index=start_idx.unsqueeze(2)).squeeze(2)
|
|
end_x = torch.gather(sorted_all_x, dim=2, index=end_idx.unsqueeze(2)).squeeze(2)
|
|
start_idx2 = torch.where(
|
|
torch.eq(x_idx, 0),
|
|
torch.tensor(0, device=x.device),
|
|
torch.where(
|
|
torch.eq(x_idx, K), torch.tensor(K - 2, device=x.device), cand_start_idx,
|
|
),
|
|
)
|
|
y_positions_expanded = yp.unsqueeze(0).expand(N, -1, -1)
|
|
start_y = torch.gather(y_positions_expanded, dim=2, index=start_idx2.unsqueeze(2)).squeeze(2)
|
|
end_y = torch.gather(y_positions_expanded, dim=2, index=(start_idx2 + 1).unsqueeze(2)).squeeze(2)
|
|
cand = start_y + (x - start_x) * (end_y - start_y) / (end_x - start_x)
|
|
return cand
|
|
|
|
|
|
def expand_dims(v, dims):
|
|
"""
|
|
Expand the tensor `v` to the dim `dims`.
|
|
|
|
Args:
|
|
`v`: a PyTorch tensor with shape [N].
|
|
`dim`: a `int`.
|
|
Returns:
|
|
a PyTorch tensor with shape [N, 1, 1, ..., 1] and the total dimension is `dims`.
|
|
"""
|
|
return v[(...,) + (None,)*(dims - 1)]
|
|
|
|
|
|
|
|
def sample_unipc(model, noise, image, sigmas, sampling_function, max_denoise, extra_args=None, callback=None, disable=None, noise_mask=None, variant='bh1'):
|
|
to_zero = False
|
|
if sigmas[-1] == 0:
|
|
timesteps = torch.nn.functional.interpolate(sigmas[None,None,:-1], size=(len(sigmas),), mode='linear')[0][0]
|
|
to_zero = True
|
|
else:
|
|
timesteps = sigmas.clone()
|
|
|
|
for s in range(timesteps.shape[0]):
|
|
timesteps[s] = (model.sigma_to_t(timesteps[s]) / 1000) + (1 / len(model.sigmas))
|
|
|
|
ns = NoiseScheduleVP('discrete', alphas_cumprod=model.inner_model.alphas_cumprod)
|
|
|
|
if image is not None:
|
|
img = image * ns.marginal_alpha(timesteps[0])
|
|
if max_denoise:
|
|
noise_mult = 1.0
|
|
else:
|
|
noise_mult = ns.marginal_std(timesteps[0])
|
|
img += noise * noise_mult
|
|
else:
|
|
img = noise
|
|
|
|
if to_zero:
|
|
timesteps[-1] = (1 / len(model.sigmas))
|
|
|
|
device = noise.device
|
|
|
|
if model.parameterization == "v":
|
|
model_type = "v"
|
|
else:
|
|
model_type = "noise"
|
|
|
|
model_fn = model_wrapper(
|
|
model.inner_model.inner_model.apply_model,
|
|
sampling_function,
|
|
ns,
|
|
model_type=model_type,
|
|
guidance_type="uncond",
|
|
model_kwargs=extra_args,
|
|
)
|
|
|
|
order = min(3, len(timesteps) - 1)
|
|
uni_pc = UniPC(model_fn, ns, predict_x0=True, thresholding=False, noise_mask=noise_mask, masked_image=image, noise=noise, variant=variant)
|
|
x = uni_pc.sample(img, timesteps=timesteps, skip_type="time_uniform", method="multistep", order=order, lower_order_final=True)
|
|
if not to_zero:
|
|
x /= ns.marginal_alpha(timesteps[-1])
|
|
return x
|