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diff --git a/ldm/models/diffusion/dpm_solver/dpm_solver.py b/ldm/models/diffusion/dpm_solver/dpm_solver.py deleted file mode 100644 index bdb64e0c..00000000 --- a/ldm/models/diffusion/dpm_solver/dpm_solver.py +++ /dev/null @@ -1,1184 +0,0 @@ -import torch -import torch.nn.functional as F -import math - - -class NoiseScheduleVP: - def __init__( - self, - schedule='discrete', - betas=None, - alphas_cumprod=None, - continuous_beta_0=0.1, - continuous_beta_1=20., - ): - """Create a wrapper class for the forward SDE (VP type). - - *** - Update: We support discrete-time diffusion models by implementing a picewise linear interpolation for log_alpha_t. - We recommend to use schedule='discrete' for the discrete-time diffusion models, especially for high-resolution images. - *** - - The forward SDE ensures that the condition distribution q_{t|0}(x_t | x_0) = N ( alpha_t * x_0, sigma_t^2 * I ). - We further define lambda_t = log(alpha_t) - log(sigma_t), which is the half-logSNR (described in the DPM-Solver paper). - Therefore, we implement the functions for computing alpha_t, sigma_t and lambda_t. For t in [0, T], we have: - - log_alpha_t = self.marginal_log_mean_coeff(t) - sigma_t = self.marginal_std(t) - lambda_t = self.marginal_lambda(t) - - Moreover, as lambda(t) is an invertible function, we also support its inverse function: - - t = self.inverse_lambda(lambda_t) - - =============================================================== - - We support both discrete-time DPMs (trained on n = 0, 1, ..., N-1) and continuous-time DPMs (trained on t in [t_0, T]). - - 1. For discrete-time DPMs: - - For discrete-time DPMs trained on n = 0, 1, ..., N-1, we convert the discrete steps to continuous time steps by: - t_i = (i + 1) / N - e.g. for N = 1000, we have t_0 = 1e-3 and T = t_{N-1} = 1. - We solve the corresponding diffusion ODE from time T = 1 to time t_0 = 1e-3. - - Args: - betas: A `torch.Tensor`. The beta array for the discrete-time DPM. (See the original DDPM paper for details) - alphas_cumprod: A `torch.Tensor`. The cumprod alphas for the discrete-time DPM. (See the original DDPM paper for details) - - Note that we always have alphas_cumprod = cumprod(betas). Therefore, we only need to set one of `betas` and `alphas_cumprod`. - - **Important**: Please pay special attention for the args for `alphas_cumprod`: - The `alphas_cumprod` is the \hat{alpha_n} arrays in the notations of DDPM. Specifically, DDPMs assume that - q_{t_n | 0}(x_{t_n} | x_0) = N ( \sqrt{\hat{alpha_n}} * x_0, (1 - \hat{alpha_n}) * I ). - Therefore, the notation \hat{alpha_n} is different from the notation alpha_t in DPM-Solver. In fact, we have - alpha_{t_n} = \sqrt{\hat{alpha_n}}, - and - log(alpha_{t_n}) = 0.5 * log(\hat{alpha_n}). - - - 2. For continuous-time DPMs: - - We support two types of VPSDEs: linear (DDPM) and cosine (improved-DDPM). The hyperparameters for the noise - schedule are the default settings in DDPM and improved-DDPM: - - Args: - beta_min: A `float` number. The smallest beta for the linear schedule. - beta_max: A `float` number. The largest beta for the linear schedule. - cosine_s: A `float` number. The hyperparameter in the cosine schedule. - cosine_beta_max: A `float` number. The hyperparameter in the cosine schedule. - T: A `float` number. The ending time of the forward process. - - =============================================================== - - Args: - schedule: A `str`. The noise schedule of the forward SDE. 'discrete' for discrete-time DPMs, - 'linear' or 'cosine' for continuous-time DPMs. - Returns: - A wrapper object of the forward SDE (VP type). - - =============================================================== - - Example: - - # For discrete-time DPMs, given betas (the beta array for n = 0, 1, ..., N - 1): - >>> ns = NoiseScheduleVP('discrete', betas=betas) - - # For discrete-time DPMs, given alphas_cumprod (the \hat{alpha_n} array for n = 0, 1, ..., N - 1): - >>> ns = NoiseScheduleVP('discrete', alphas_cumprod=alphas_cumprod) - - # For continuous-time DPMs (VPSDE), linear schedule: - >>> ns = NoiseScheduleVP('linear', continuous_beta_0=0.1, continuous_beta_1=20.) - - """ - - if schedule not in ['discrete', 'linear', 'cosine']: - raise ValueError("Unsupported noise schedule {}. The schedule needs to be 'discrete' or 'linear' or 'cosine'".format(schedule)) - - self.schedule = schedule - if schedule == 'discrete': - if betas is not None: - log_alphas = 0.5 * torch.log(1 - betas).cumsum(dim=0) - else: - assert alphas_cumprod is not None - log_alphas = 0.5 * torch.log(alphas_cumprod) - self.total_N = len(log_alphas) - self.T = 1. - self.t_array = torch.linspace(0., 1., self.total_N + 1)[1:].reshape((1, -1)) - self.log_alpha_array = log_alphas.reshape((1, -1,)) - else: - self.total_N = 1000 - self.beta_0 = continuous_beta_0 - self.beta_1 = continuous_beta_1 - self.cosine_s = 0.008 - self.cosine_beta_max = 999. - 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 - self.cosine_log_alpha_0 = math.log(math.cos(self.cosine_s / (1. + self.cosine_s) * math.pi / 2.)) - self.schedule = schedule - if schedule == 'cosine': - # For the cosine schedule, T = 1 will have numerical issues. So we manually set the ending time T. - # Note that T = 0.9946 may be not the optimal setting. However, we find it works well. - self.T = 0.9946 - else: - self.T = 1. - - def marginal_log_mean_coeff(self, t): - """ - Compute log(alpha_t) of a given continuous-time label t in [0, T]. - """ - if self.schedule == 'discrete': - return interpolate_fn(t.reshape((-1, 1)), self.t_array.to(t.device), self.log_alpha_array.to(t.device)).reshape((-1)) - elif self.schedule == 'linear': - return -0.25 * t ** 2 * (self.beta_1 - self.beta_0) - 0.5 * t * self.beta_0 - elif self.schedule == 'cosine': - log_alpha_fn = lambda s: torch.log(torch.cos((s + self.cosine_s) / (1. + self.cosine_s) * math.pi / 2.)) - log_alpha_t = log_alpha_fn(t) - self.cosine_log_alpha_0 - return log_alpha_t - - def marginal_alpha(self, t): - """ - Compute alpha_t of a given continuous-time label t in [0, T]. - """ - return torch.exp(self.marginal_log_mean_coeff(t)) - - def marginal_std(self, t): - """ - Compute sigma_t of a given continuous-time label t in [0, T]. - """ - return torch.sqrt(1. - torch.exp(2. * self.marginal_log_mean_coeff(t))) - - def marginal_lambda(self, t): - """ - Compute lambda_t = log(alpha_t) - log(sigma_t) of a given continuous-time label t in [0, T]. - """ - log_mean_coeff = self.marginal_log_mean_coeff(t) - log_std = 0.5 * torch.log(1. - torch.exp(2. * log_mean_coeff)) - return log_mean_coeff - log_std - - def inverse_lambda(self, lamb): - """ - Compute the continuous-time label t in [0, T] of a given half-logSNR lambda_t. - """ - if self.schedule == 'linear': - tmp = 2. * (self.beta_1 - self.beta_0) * torch.logaddexp(-2. * lamb, torch.zeros((1,)).to(lamb)) - Delta = self.beta_0**2 + tmp - return tmp / (torch.sqrt(Delta) + self.beta_0) / (self.beta_1 - self.beta_0) - elif self.schedule == 'discrete': - log_alpha = -0.5 * torch.logaddexp(torch.zeros((1,)).to(lamb.device), -2. * lamb) - 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])) - return t.reshape((-1,)) - else: - log_alpha = -0.5 * torch.logaddexp(-2. * lamb, torch.zeros((1,)).to(lamb)) - 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 - t = t_fn(log_alpha) - return t - - -def model_wrapper( - model, - noise_schedule, - model_type="noise", - model_kwargs={}, - guidance_type="uncond", - condition=None, - unconditional_condition=None, - guidance_scale=1., - classifier_fn=None, - classifier_kwargs={}, -): - """Create a wrapper function for the noise prediction model. - - DPM-Solver needs to solve the continuous-time diffusion ODEs. For DPMs trained on discrete-time labels, we need to - firstly wrap the model function to a noise prediction model that accepts the continuous time as the input. - - We support four types of the diffusion model by setting `model_type`: - - 1. "noise": noise prediction model. (Trained by predicting noise). - - 2. "x_start": data prediction model. (Trained by predicting the data x_0 at time 0). - - 3. "v": velocity prediction model. (Trained by predicting the velocity). - The "v" prediction is derivation detailed in Appendix D of [1], and is used in Imagen-Video [2]. - - [1] Salimans, Tim, and Jonathan Ho. "Progressive distillation for fast sampling of diffusion models." - arXiv preprint arXiv:2202.00512 (2022). - [2] Ho, Jonathan, et al. "Imagen Video: High Definition Video Generation with Diffusion Models." - arXiv preprint arXiv:2210.02303 (2022). - - 4. "score": marginal score function. (Trained by denoising score matching). - Note that the score function and the noise prediction model follows a simple relationship: - ``` - noise(x_t, t) = -sigma_t * score(x_t, t) - ``` - - We support three types of guided sampling by DPMs by setting `guidance_type`: - 1. "uncond": unconditional sampling by DPMs. - The input `model` has the following format: - `` - model(x, t_input, **model_kwargs) -> noise | x_start | v | score - `` - - 2. "classifier": classifier guidance sampling [3] by DPMs and another classifier. - The input `model` has the following format: - `` - model(x, t_input, **model_kwargs) -> noise | x_start | v | score - `` - - The input `classifier_fn` has the following format: - `` - classifier_fn(x, t_input, cond, **classifier_kwargs) -> logits(x, t_input, cond) - `` - - [3] P. Dhariwal and A. Q. Nichol, "Diffusion models beat GANs on image synthesis," - in Advances in Neural Information Processing Systems, vol. 34, 2021, pp. 8780-8794. - - 3. "classifier-free": classifier-free guidance sampling by conditional DPMs. - The input `model` has the following format: - `` - model(x, t_input, cond, **model_kwargs) -> noise | x_start | v | score - `` - And if cond == `unconditional_condition`, the model output is the unconditional DPM output. - - [4] Ho, Jonathan, and Tim Salimans. "Classifier-free diffusion guidance." - arXiv preprint arXiv:2207.12598 (2022). - - - The `t_input` is the time label of the model, which may be discrete-time labels (i.e. 0 to 999) - or continuous-time labels (i.e. epsilon to T). - - We wrap the model function to accept only `x` and `t_continuous` as inputs, and outputs the predicted noise: - `` - def model_fn(x, t_continuous) -> noise: - t_input = get_model_input_time(t_continuous) - return noise_pred(model, x, t_input, **model_kwargs) - `` - where `t_continuous` is the continuous time labels (i.e. epsilon to T). And we use `model_fn` for DPM-Solver. - - =============================================================== - - Args: - model: A diffusion model with the corresponding format described above. - noise_schedule: A noise schedule object, such as NoiseScheduleVP. - model_type: A `str`. The parameterization type of the diffusion model. - "noise" or "x_start" or "v" or "score". - model_kwargs: A `dict`. A dict for the other inputs of the model function. - guidance_type: A `str`. The type of the guidance for sampling. - "uncond" or "classifier" or "classifier-free". - condition: A pytorch tensor. The condition for the guided sampling. - Only used for "classifier" or "classifier-free" guidance type. - unconditional_condition: A pytorch tensor. The condition for the unconditional sampling. - Only used for "classifier-free" guidance type. - guidance_scale: A `float`. The scale for the guided sampling. - classifier_fn: A classifier function. Only used for the classifier guidance. - classifier_kwargs: A `dict`. A dict for the other inputs of the classifier function. - Returns: - A noise prediction model that accepts the noised data and the continuous time as the inputs. - """ - - def get_model_input_time(t_continuous): - """ - Convert the continuous-time `t_continuous` (in [epsilon, T]) to the model input time. - For discrete-time DPMs, we convert `t_continuous` in [1 / N, 1] to `t_input` in [0, 1000 * (N - 1) / N]. - For continuous-time DPMs, we just use `t_continuous`. - """ - if noise_schedule.schedule == 'discrete': - return (t_continuous - 1. / noise_schedule.total_N) * 1000. - else: - return t_continuous - - def noise_pred_fn(x, t_continuous, cond=None): - if t_continuous.reshape((-1,)).shape[0] == 1: - t_continuous = t_continuous.expand((x.shape[0])) - t_input = get_model_input_time(t_continuous) - if cond is None: - output = model(x, t_input, **model_kwargs) - else: - output = model(x, t_input, cond, **model_kwargs) - if model_type == "noise": - return output - elif model_type == "x_start": - alpha_t, sigma_t = noise_schedule.marginal_alpha(t_continuous), noise_schedule.marginal_std(t_continuous) - dims = x.dim() - return (x - expand_dims(alpha_t, dims) * output) / expand_dims(sigma_t, dims) - elif model_type == "v": - alpha_t, sigma_t = noise_schedule.marginal_alpha(t_continuous), noise_schedule.marginal_std(t_continuous) - dims = x.dim() - return expand_dims(alpha_t, dims) * output + expand_dims(sigma_t, dims) * x - elif model_type == "score": - sigma_t = noise_schedule.marginal_std(t_continuous) - dims = x.dim() - return -expand_dims(sigma_t, dims) * output - - def cond_grad_fn(x, t_input): - """ - Compute the gradient of the classifier, i.e. nabla_{x} log p_t(cond | x_t). - """ - with torch.enable_grad(): - x_in = x.detach().requires_grad_(True) - log_prob = classifier_fn(x_in, t_input, condition, **classifier_kwargs) - return torch.autograd.grad(log_prob.sum(), x_in)[0] - - def model_fn(x, t_continuous): - """ - The noise predicition model function that is used for DPM-Solver. - """ - if t_continuous.reshape((-1,)).shape[0] == 1: - t_continuous = t_continuous.expand((x.shape[0])) - if guidance_type == "uncond": - return noise_pred_fn(x, t_continuous) - elif guidance_type == "classifier": - assert classifier_fn is not None - t_input = get_model_input_time(t_continuous) - cond_grad = cond_grad_fn(x, t_input) - sigma_t = noise_schedule.marginal_std(t_continuous) - noise = noise_pred_fn(x, t_continuous) - return noise - guidance_scale * expand_dims(sigma_t, dims=cond_grad.dim()) * cond_grad - elif guidance_type == "classifier-free": - if guidance_scale == 1. or unconditional_condition is None: - return noise_pred_fn(x, t_continuous, cond=condition) - else: - x_in = torch.cat([x] * 2) - t_in = torch.cat([t_continuous] * 2) - c_in = torch.cat([unconditional_condition, condition]) - noise_uncond, noise = noise_pred_fn(x_in, t_in, cond=c_in).chunk(2) - return noise_uncond + guidance_scale * (noise - noise_uncond) - - assert model_type in ["noise", "x_start", "v"] - assert guidance_type in ["uncond", "classifier", "classifier-free"] - return model_fn - - -class DPM_Solver: - def __init__(self, model_fn, noise_schedule, predict_x0=False, thresholding=False, max_val=1.): - """Construct a DPM-Solver. - - We support both the noise prediction model ("predicting epsilon") and the data prediction model ("predicting x0"). - If `predict_x0` is False, we use the solver for the noise prediction model (DPM-Solver). - If `predict_x0` is True, we use the solver for the data prediction model (DPM-Solver++). - In such case, we further support the "dynamic thresholding" in [1] when `thresholding` is True. - The "dynamic thresholding" can greatly improve the sample quality for pixel-space DPMs with large guidance scales. - - Args: - model_fn: A noise prediction model function which accepts the continuous-time input (t in [epsilon, T]): - `` - def model_fn(x, t_continuous): - return noise - `` - noise_schedule: A noise schedule object, such as NoiseScheduleVP. - predict_x0: A `bool`. If true, use the data prediction model; else, use the noise prediction model. - thresholding: A `bool`. Valid when `predict_x0` is True. Whether to use the "dynamic thresholding" in [1]. - max_val: A `float`. Valid when both `predict_x0` and `thresholding` are True. The max value for thresholding. - - [1] Chitwan Saharia, William Chan, Saurabh Saxena, Lala Li, Jay Whang, Emily Denton, Seyed Kamyar Seyed Ghasemipour, Burcu Karagol Ayan, S Sara Mahdavi, Rapha Gontijo Lopes, et al. Photorealistic text-to-image diffusion models with deep language understanding. arXiv preprint arXiv:2205.11487, 2022b. - """ - self.model = model_fn - self.noise_schedule = noise_schedule - self.predict_x0 = predict_x0 - self.thresholding = thresholding - self.max_val = max_val - - def noise_prediction_fn(self, x, t): - """ - Return the noise prediction model. - """ - return self.model(x, t) - - def data_prediction_fn(self, x, t): - """ - Return the data prediction model (with thresholding). - """ - noise = self.noise_prediction_fn(x, t) - dims = x.dim() - alpha_t, sigma_t = self.noise_schedule.marginal_alpha(t), self.noise_schedule.marginal_std(t) - x0 = (x - expand_dims(sigma_t, dims) * noise) / expand_dims(alpha_t, dims) - if self.thresholding: - p = 0.995 # A hyperparameter in the paper of "Imagen" [1]. - s = torch.quantile(torch.abs(x0).reshape((x0.shape[0], -1)), p, dim=1) - s = expand_dims(torch.maximum(s, self.max_val * torch.ones_like(s).to(s.device)), dims) - x0 = torch.clamp(x0, -s, s) / s - 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. - - Args: - skip_type: A `str`. The type for the spacing of the time steps. We support three types: - - 'logSNR': uniform logSNR for the time steps. - - 'time_uniform': uniform time for the time steps. (**Recommended for high-resolutional data**.) - - 'time_quadratic': quadratic time for the time steps. (Used in DDIM for low-resolutional data.) - t_T: A `float`. The starting time of the sampling (default is T). - t_0: A `float`. The ending time of the sampling (default is epsilon). - N: A `int`. The total number of the spacing of the time steps. - device: A torch device. - Returns: - A pytorch tensor of the time steps, with the shape (N + 1,). - """ - 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. - - We combine both DPM-Solver-1,2,3 to use all the function evaluations, which is named as "DPM-Solver-fast". - Given a fixed number of function evaluations by `steps`, the sampling procedure by DPM-Solver-fast is: - - If order == 1: - We take `steps` of DPM-Solver-1 (i.e. DDIM). - - If order == 2: - - Denote K = (steps // 2). We take K or (K + 1) intermediate time steps for sampling. - - If steps % 2 == 0, we use K steps of DPM-Solver-2. - - If steps % 2 == 1, we use K steps of DPM-Solver-2 and 1 step of DPM-Solver-1. - - If order == 3: - - Denote K = (steps // 3 + 1). We take K intermediate time steps for sampling. - - If steps % 3 == 0, we use (K - 2) steps of DPM-Solver-3, and 1 step of DPM-Solver-2 and 1 step of DPM-Solver-1. - - If steps % 3 == 1, we use (K - 1) steps of DPM-Solver-3 and 1 step of DPM-Solver-1. - - If steps % 3 == 2, we use (K - 1) steps of DPM-Solver-3 and 1 step of DPM-Solver-2. - - ============================================ - Args: - order: A `int`. The max order for the solver (2 or 3). - steps: A `int`. The total number of function evaluations (NFE). - skip_type: A `str`. The type for the spacing of the time steps. We support three types: - - 'logSNR': uniform logSNR for the time steps. - - 'time_uniform': uniform time for the time steps. (**Recommended for high-resolutional data**.) - - 'time_quadratic': quadratic time for the time steps. (Used in DDIM for low-resolutional data.) - t_T: A `float`. The starting time of the sampling (default is T). - t_0: A `float`. The ending time of the sampling (default is epsilon). - device: A torch device. - Returns: - orders: A list of the solver order of each step. - """ - 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 = 1 - 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)).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 dpm_solver_first_update(self, x, s, t, model_s=None, return_intermediate=False): - """ - DPM-Solver-1 (equivalent to DDIM) from time `s` to time `t`. - - Args: - x: A pytorch tensor. The initial value at time `s`. - s: A pytorch tensor. The starting time, with the shape (x.shape[0],). - t: A pytorch tensor. The ending time, with the shape (x.shape[0],). - model_s: A pytorch tensor. The model function evaluated at time `s`. - If `model_s` is None, we evaluate the model by `x` and `s`; otherwise we directly use it. - return_intermediate: A `bool`. If true, also return the model value at time `s`. - Returns: - x_t: A pytorch tensor. The approximated solution at time `t`. - """ - ns = self.noise_schedule - dims = x.dim() - lambda_s, lambda_t = ns.marginal_lambda(s), ns.marginal_lambda(t) - h = lambda_t - lambda_s - log_alpha_s, log_alpha_t = ns.marginal_log_mean_coeff(s), ns.marginal_log_mean_coeff(t) - sigma_s, sigma_t = ns.marginal_std(s), ns.marginal_std(t) - alpha_t = torch.exp(log_alpha_t) - - if self.predict_x0: - phi_1 = torch.expm1(-h) - if model_s is None: - model_s = self.model_fn(x, s) - x_t = ( - expand_dims(sigma_t / sigma_s, dims) * x - - expand_dims(alpha_t * phi_1, dims) * model_s - ) - if return_intermediate: - return x_t, {'model_s': model_s} - else: - return x_t - else: - phi_1 = torch.expm1(h) - if model_s is None: - model_s = self.model_fn(x, s) - x_t = ( - expand_dims(torch.exp(log_alpha_t - log_alpha_s), dims) * x - - expand_dims(sigma_t * phi_1, dims) * model_s - ) - if return_intermediate: - return x_t, {'model_s': model_s} - else: - return x_t - - def singlestep_dpm_solver_second_update(self, x, s, t, r1=0.5, model_s=None, return_intermediate=False, solver_type='dpm_solver'): - """ - Singlestep solver DPM-Solver-2 from time `s` to time `t`. - - Args: - x: A pytorch tensor. The initial value at time `s`. - s: A pytorch tensor. The starting time, with the shape (x.shape[0],). - t: A pytorch tensor. The ending time, with the shape (x.shape[0],). - r1: A `float`. The hyperparameter of the second-order solver. - model_s: A pytorch tensor. The model function evaluated at time `s`. - If `model_s` is None, we evaluate the model by `x` and `s`; otherwise we directly use it. - return_intermediate: A `bool`. If true, also return the model value at time `s` and `s1` (the intermediate time). - solver_type: either 'dpm_solver' or 'taylor'. The type for the high-order solvers. - The type slightly impacts the performance. We recommend to use 'dpm_solver' type. - Returns: - x_t: A pytorch tensor. The approximated solution at time `t`. - """ - if solver_type not in ['dpm_solver', 'taylor']: - raise ValueError("'solver_type' must be either 'dpm_solver' or 'taylor', got {}".format(solver_type)) - if r1 is None: - r1 = 0.5 - ns = self.noise_schedule - dims = x.dim() - lambda_s, lambda_t = ns.marginal_lambda(s), ns.marginal_lambda(t) - h = lambda_t - lambda_s - lambda_s1 = lambda_s + r1 * h - s1 = ns.inverse_lambda(lambda_s1) - log_alpha_s, log_alpha_s1, log_alpha_t = ns.marginal_log_mean_coeff(s), ns.marginal_log_mean_coeff(s1), ns.marginal_log_mean_coeff(t) - sigma_s, sigma_s1, sigma_t = ns.marginal_std(s), ns.marginal_std(s1), ns.marginal_std(t) - alpha_s1, alpha_t = torch.exp(log_alpha_s1), torch.exp(log_alpha_t) - - if self.predict_x0: - phi_11 = torch.expm1(-r1 * h) - phi_1 = torch.expm1(-h) - - if model_s is None: - model_s = self.model_fn(x, s) - x_s1 = ( - expand_dims(sigma_s1 / sigma_s, dims) * x - - expand_dims(alpha_s1 * phi_11, dims) * model_s - ) - model_s1 = self.model_fn(x_s1, s1) - if solver_type == 'dpm_solver': - x_t = ( - expand_dims(sigma_t / sigma_s, dims) * x - - expand_dims(alpha_t * phi_1, dims) * model_s - - (0.5 / r1) * expand_dims(alpha_t * phi_1, dims) * (model_s1 - model_s) - ) - elif solver_type == 'taylor': - x_t = ( - expand_dims(sigma_t / sigma_s, dims) * x - - expand_dims(alpha_t * phi_1, dims) * model_s - + (1. / r1) * expand_dims(alpha_t * ((torch.exp(-h) - 1.) / h + 1.), dims) * (model_s1 - model_s) - ) - else: - phi_11 = torch.expm1(r1 * h) - phi_1 = torch.expm1(h) - - if model_s is None: - model_s = self.model_fn(x, s) - x_s1 = ( - expand_dims(torch.exp(log_alpha_s1 - log_alpha_s), dims) * x - - expand_dims(sigma_s1 * phi_11, dims) * model_s - ) - model_s1 = self.model_fn(x_s1, s1) - if solver_type == 'dpm_solver': - x_t = ( - expand_dims(torch.exp(log_alpha_t - log_alpha_s), dims) * x - - expand_dims(sigma_t * phi_1, dims) * model_s - - (0.5 / r1) * expand_dims(sigma_t * phi_1, dims) * (model_s1 - model_s) - ) - elif solver_type == 'taylor': - x_t = ( - expand_dims(torch.exp(log_alpha_t - log_alpha_s), dims) * x - - expand_dims(sigma_t * phi_1, dims) * model_s - - (1. / r1) * expand_dims(sigma_t * ((torch.exp(h) - 1.) / h - 1.), dims) * (model_s1 - model_s) - ) - if return_intermediate: - return x_t, {'model_s': model_s, 'model_s1': model_s1} - else: - return x_t - - def singlestep_dpm_solver_third_update(self, x, s, t, r1=1./3., r2=2./3., model_s=None, model_s1=None, return_intermediate=False, solver_type='dpm_solver'): - """ - Singlestep solver DPM-Solver-3 from time `s` to time `t`. - - Args: - x: A pytorch tensor. The initial value at time `s`. - s: A pytorch tensor. The starting time, with the shape (x.shape[0],). - t: A pytorch tensor. The ending time, with the shape (x.shape[0],). - r1: A `float`. The hyperparameter of the third-order solver. - r2: A `float`. The hyperparameter of the third-order solver. - model_s: A pytorch tensor. The model function evaluated at time `s`. - If `model_s` is None, we evaluate the model by `x` and `s`; otherwise we directly use it. - model_s1: A pytorch tensor. The model function evaluated at time `s1` (the intermediate time given by `r1`). - If `model_s1` is None, we evaluate the model at `s1`; otherwise we directly use it. - return_intermediate: A `bool`. If true, also return the model value at time `s`, `s1` and `s2` (the intermediate times). - solver_type: either 'dpm_solver' or 'taylor'. The type for the high-order solvers. - The type slightly impacts the performance. We recommend to use 'dpm_solver' type. - Returns: - x_t: A pytorch tensor. The approximated solution at time `t`. - """ - if solver_type not in ['dpm_solver', 'taylor']: - raise ValueError("'solver_type' must be either 'dpm_solver' or 'taylor', got {}".format(solver_type)) - if r1 is None: - r1 = 1. / 3. - if r2 is None: - r2 = 2. / 3. - ns = self.noise_schedule - dims = x.dim() - lambda_s, lambda_t = ns.marginal_lambda(s), ns.marginal_lambda(t) - h = lambda_t - lambda_s - lambda_s1 = lambda_s + r1 * h - lambda_s2 = lambda_s + r2 * h - s1 = ns.inverse_lambda(lambda_s1) - s2 = ns.inverse_lambda(lambda_s2) - log_alpha_s, log_alpha_s1, log_alpha_s2, log_alpha_t = ns.marginal_log_mean_coeff(s), ns.marginal_log_mean_coeff(s1), ns.marginal_log_mean_coeff(s2), ns.marginal_log_mean_coeff(t) - sigma_s, sigma_s1, sigma_s2, sigma_t = ns.marginal_std(s), ns.marginal_std(s1), ns.marginal_std(s2), ns.marginal_std(t) - alpha_s1, alpha_s2, alpha_t = torch.exp(log_alpha_s1), torch.exp(log_alpha_s2), torch.exp(log_alpha_t) - - if self.predict_x0: - phi_11 = torch.expm1(-r1 * h) - phi_12 = torch.expm1(-r2 * h) - phi_1 = torch.expm1(-h) - phi_22 = torch.expm1(-r2 * h) / (r2 * h) + 1. - phi_2 = phi_1 / h + 1. - phi_3 = phi_2 / h - 0.5 - - if model_s is None: - model_s = self.model_fn(x, s) - if model_s1 is None: - x_s1 = ( - expand_dims(sigma_s1 / sigma_s, dims) * x - - expand_dims(alpha_s1 * phi_11, dims) * model_s - ) - model_s1 = self.model_fn(x_s1, s1) - x_s2 = ( - expand_dims(sigma_s2 / sigma_s, dims) * x - - expand_dims(alpha_s2 * phi_12, dims) * model_s - + r2 / r1 * expand_dims(alpha_s2 * phi_22, dims) * (model_s1 - model_s) - ) - model_s2 = self.model_fn(x_s2, s2) - if solver_type == 'dpm_solver': - x_t = ( - expand_dims(sigma_t / sigma_s, dims) * x - - expand_dims(alpha_t * phi_1, dims) * model_s - + (1. / r2) * expand_dims(alpha_t * phi_2, dims) * (model_s2 - model_s) - ) - elif solver_type == 'taylor': - D1_0 = (1. / r1) * (model_s1 - model_s) - D1_1 = (1. / r2) * (model_s2 - model_s) - D1 = (r2 * D1_0 - r1 * D1_1) / (r2 - r1) - D2 = 2. * (D1_1 - D1_0) / (r2 - r1) - x_t = ( - expand_dims(sigma_t / sigma_s, dims) * x - - expand_dims(alpha_t * phi_1, dims) * model_s - + expand_dims(alpha_t * phi_2, dims) * D1 - - expand_dims(alpha_t * phi_3, dims) * D2 - ) - else: - phi_11 = torch.expm1(r1 * h) - phi_12 = torch.expm1(r2 * h) - phi_1 = torch.expm1(h) - phi_22 = torch.expm1(r2 * h) / (r2 * h) - 1. - phi_2 = phi_1 / h - 1. - phi_3 = phi_2 / h - 0.5 - - if model_s is None: - model_s = self.model_fn(x, s) - if model_s1 is None: - x_s1 = ( - expand_dims(torch.exp(log_alpha_s1 - log_alpha_s), dims) * x - - expand_dims(sigma_s1 * phi_11, dims) * model_s - ) - model_s1 = self.model_fn(x_s1, s1) - x_s2 = ( - expand_dims(torch.exp(log_alpha_s2 - log_alpha_s), dims) * x - - expand_dims(sigma_s2 * phi_12, dims) * model_s - - r2 / r1 * expand_dims(sigma_s2 * phi_22, dims) * (model_s1 - model_s) - ) - model_s2 = self.model_fn(x_s2, s2) - if solver_type == 'dpm_solver': - x_t = ( - expand_dims(torch.exp(log_alpha_t - log_alpha_s), dims) * x - - expand_dims(sigma_t * phi_1, dims) * model_s - - (1. / r2) * expand_dims(sigma_t * phi_2, dims) * (model_s2 - model_s) - ) - elif solver_type == 'taylor': - D1_0 = (1. / r1) * (model_s1 - model_s) - D1_1 = (1. / r2) * (model_s2 - model_s) - D1 = (r2 * D1_0 - r1 * D1_1) / (r2 - r1) - D2 = 2. * (D1_1 - D1_0) / (r2 - r1) - x_t = ( - expand_dims(torch.exp(log_alpha_t - log_alpha_s), dims) * x - - expand_dims(sigma_t * phi_1, dims) * model_s - - expand_dims(sigma_t * phi_2, dims) * D1 - - expand_dims(sigma_t * phi_3, dims) * D2 - ) - - if return_intermediate: - return x_t, {'model_s': model_s, 'model_s1': model_s1, 'model_s2': model_s2} - else: - return x_t - - def multistep_dpm_solver_second_update(self, x, model_prev_list, t_prev_list, t, solver_type="dpm_solver"): - """ - Multistep solver DPM-Solver-2 from time `t_prev_list[-1]` to time `t`. - - Args: - x: A pytorch tensor. The initial value at time `s`. - model_prev_list: A list of pytorch tensor. The previous computed model values. - t_prev_list: A list of pytorch tensor. The previous times, each time has the shape (x.shape[0],) - t: A pytorch tensor. The ending time, with the shape (x.shape[0],). - solver_type: either 'dpm_solver' or 'taylor'. The type for the high-order solvers. - The type slightly impacts the performance. We recommend to use 'dpm_solver' type. - Returns: - x_t: A pytorch tensor. The approximated solution at time `t`. - """ - if solver_type not in ['dpm_solver', 'taylor']: - raise ValueError("'solver_type' must be either 'dpm_solver' or 'taylor', got {}".format(solver_type)) - ns = self.noise_schedule - dims = x.dim() - model_prev_1, model_prev_0 = model_prev_list - t_prev_1, t_prev_0 = t_prev_list - lambda_prev_1, lambda_prev_0, lambda_t = ns.marginal_lambda(t_prev_1), ns.marginal_lambda(t_prev_0), ns.marginal_lambda(t) - log_alpha_prev_0, log_alpha_t = ns.marginal_log_mean_coeff(t_prev_0), ns.marginal_log_mean_coeff(t) - sigma_prev_0, sigma_t = ns.marginal_std(t_prev_0), ns.marginal_std(t) - alpha_t = torch.exp(log_alpha_t) - - h_0 = lambda_prev_0 - lambda_prev_1 - h = lambda_t - lambda_prev_0 - r0 = h_0 / h - D1_0 = expand_dims(1. / r0, dims) * (model_prev_0 - model_prev_1) - if self.predict_x0: - if solver_type == 'dpm_solver': - x_t = ( - expand_dims(sigma_t / sigma_prev_0, dims) * x - - expand_dims(alpha_t * (torch.exp(-h) - 1.), dims) * model_prev_0 - - 0.5 * expand_dims(alpha_t * (torch.exp(-h) - 1.), dims) * D1_0 - ) - elif solver_type == 'taylor': - x_t = ( - expand_dims(sigma_t / sigma_prev_0, dims) * x - - expand_dims(alpha_t * (torch.exp(-h) - 1.), dims) * model_prev_0 - + expand_dims(alpha_t * ((torch.exp(-h) - 1.) / h + 1.), dims) * D1_0 - ) - else: - if solver_type == 'dpm_solver': - x_t = ( - expand_dims(torch.exp(log_alpha_t - log_alpha_prev_0), dims) * x |