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| # Licensed under the Apache License, Version 2.0 (the "License"); | |
| # you may not use this file except in compliance with the License. | |
| # You may obtain a copy of the License at | |
| # | |
| # http://www.apache.org/licenses/LICENSE-2.0 | |
| # | |
| # Unless required by applicable law or agreed to in writing, software | |
| # distributed under the License is distributed on an "AS IS" BASIS, | |
| # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | |
| # See the License for the specific language governing permissions and | |
| # limitations under the License. | |
| # DISCLAIMER: check https://arxiv.org/abs/2309.05019 | |
| # The codebase is modified based on https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_dpmsolver_multistep.py | |
| import math | |
| from typing import List, Optional, Tuple, Union, Callable | |
| import numpy as np | |
| import torch | |
| from diffusers.configuration_utils import ConfigMixin, register_to_config | |
| from diffusers.utils.torch_utils import randn_tensor | |
| from diffusers.schedulers.scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput | |
| # Copied from diffusers.schedulers.scheduling_ddpm.betas_for_alpha_bar | |
| def betas_for_alpha_bar( | |
| num_diffusion_timesteps, | |
| max_beta=0.999, | |
| alpha_transform_type="cosine", | |
| ): | |
| """ | |
| Create a beta schedule that discretizes the given alpha_t_bar function, which defines the cumulative product of | |
| (1-beta) over time from t = [0,1]. | |
| Contains a function alpha_bar that takes an argument t and transforms it to the cumulative product of (1-beta) up | |
| to that part of the diffusion process. | |
| Args: | |
| num_diffusion_timesteps (`int`): the number of betas to produce. | |
| max_beta (`float`): the maximum beta to use; use values lower than 1 to | |
| prevent singularities. | |
| alpha_transform_type (`str`, *optional*, default to `cosine`): the type of noise schedule for alpha_bar. | |
| Choose from `cosine` or `exp` | |
| Returns: | |
| betas (`np.ndarray`): the betas used by the scheduler to step the model outputs | |
| """ | |
| if alpha_transform_type == "cosine": | |
| def alpha_bar_fn(t): | |
| return math.cos((t + 0.008) / 1.008 * math.pi / 2) ** 2 | |
| elif alpha_transform_type == "exp": | |
| def alpha_bar_fn(t): | |
| return math.exp(t * -12.0) | |
| else: | |
| raise ValueError(f"Unsupported alpha_tranform_type: {alpha_transform_type}") | |
| betas = [] | |
| for i in range(num_diffusion_timesteps): | |
| t1 = i / num_diffusion_timesteps | |
| t2 = (i + 1) / num_diffusion_timesteps | |
| betas.append(min(1 - alpha_bar_fn(t2) / alpha_bar_fn(t1), max_beta)) | |
| return torch.tensor(betas, dtype=torch.float32) | |
| class SASolverScheduler(SchedulerMixin, ConfigMixin): | |
| """ | |
| `SASolverScheduler` is a fast dedicated high-order solver for diffusion SDEs. | |
| This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic | |
| methods the library implements for all schedulers such as loading and saving. | |
| Args: | |
| num_train_timesteps (`int`, defaults to 1000): | |
| The number of diffusion steps to train the model. | |
| beta_start (`float`, defaults to 0.0001): | |
| The starting `beta` value of inference. | |
| beta_end (`float`, defaults to 0.02): | |
| The final `beta` value. | |
| beta_schedule (`str`, defaults to `"linear"`): | |
| The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from | |
| `linear`, `scaled_linear`, or `squaredcos_cap_v2`. | |
| trained_betas (`np.ndarray`, *optional*): | |
| Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`. | |
| predictor_order (`int`, defaults to 2): | |
| The predictor order which can be `1` or `2` or `3` or '4'. It is recommended to use `predictor_order=2` for guided | |
| sampling, and `predictor_order=3` for unconditional sampling. | |
| corrector_order (`int`, defaults to 2): | |
| The corrector order which can be `1` or `2` or `3` or '4'. It is recommended to use `corrector_order=2` for guided | |
| sampling, and `corrector_order=3` for unconditional sampling. | |
| predictor_corrector_mode (`str`, defaults to `PEC`): | |
| The predictor-corrector mode can be `PEC` or 'PECE'. It is recommended to use `PEC` mode for fast | |
| sampling, and `PECE` for high-quality sampling (PECE needs around twice model evaluations as PEC). | |
| prediction_type (`str`, defaults to `epsilon`, *optional*): | |
| Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process), | |
| `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen | |
| Video](https://imagen.research.google/video/paper.pdf) paper). | |
| thresholding (`bool`, defaults to `False`): | |
| Whether to use the "dynamic thresholding" method. This is unsuitable for latent-space diffusion models such | |
| as Stable Diffusion. | |
| dynamic_thresholding_ratio (`float`, defaults to 0.995): | |
| The ratio for the dynamic thresholding method. Valid only when `thresholding=True`. | |
| sample_max_value (`float`, defaults to 1.0): | |
| The threshold value for dynamic thresholding. Valid only when `thresholding=True` and | |
| `algorithm_type="dpmsolver++"`. | |
| algorithm_type (`str`, defaults to `data_prediction`): | |
| Algorithm type for the solver; can be `data_prediction` or `noise_prediction`. It is recommended to use `data_prediction` | |
| with `solver_order=2` for guided sampling like in Stable Diffusion. | |
| lower_order_final (`bool`, defaults to `True`): | |
| Whether to use lower-order solvers in the final steps. Default = True. | |
| use_karras_sigmas (`bool`, *optional*, defaults to `False`): | |
| Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. If `True`, | |
| the sigmas are determined according to a sequence of noise levels {σi}. | |
| lambda_min_clipped (`float`, defaults to `-inf`): | |
| Clipping threshold for the minimum value of `lambda(t)` for numerical stability. This is critical for the | |
| cosine (`squaredcos_cap_v2`) noise schedule. | |
| variance_type (`str`, *optional*): | |
| Set to "learned" or "learned_range" for diffusion models that predict variance. If set, the model's output | |
| contains the predicted Gaussian variance. | |
| timestep_spacing (`str`, defaults to `"linspace"`): | |
| The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and | |
| Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information. | |
| steps_offset (`int`, defaults to 0): | |
| An offset added to the inference steps. You can use a combination of `offset=1` and | |
| `set_alpha_to_one=False` to make the last step use step 0 for the previous alpha product like in Stable | |
| Diffusion. | |
| """ | |
| _compatibles = [e.name for e in KarrasDiffusionSchedulers] | |
| order = 1 | |
| def __init__( | |
| self, | |
| num_train_timesteps: int = 1000, | |
| beta_start: float = 0.0001, | |
| beta_end: float = 0.02, | |
| beta_schedule: str = "linear", | |
| trained_betas: Optional[Union[np.ndarray, List[float]]] = None, | |
| predictor_order: int = 2, | |
| corrector_order: int = 2, | |
| predictor_corrector_mode: str = 'PEC', | |
| prediction_type: str = "epsilon", | |
| tau_func: Callable = lambda t: 1 if t >= 200 and t <= 800 else 0, | |
| thresholding: bool = False, | |
| dynamic_thresholding_ratio: float = 0.995, | |
| sample_max_value: float = 1.0, | |
| algorithm_type: str = "data_prediction", | |
| lower_order_final: bool = True, | |
| use_karras_sigmas: Optional[bool] = False, | |
| lambda_min_clipped: float = -float("inf"), | |
| variance_type: Optional[str] = None, | |
| timestep_spacing: str = "linspace", | |
| steps_offset: int = 0, | |
| ): | |
| if trained_betas is not None: | |
| self.betas = torch.tensor(trained_betas, dtype=torch.float32) | |
| elif beta_schedule == "linear": | |
| self.betas = torch.linspace(beta_start, beta_end, num_train_timesteps, dtype=torch.float32) | |
| elif beta_schedule == "scaled_linear": | |
| # this schedule is very specific to the latent diffusion model. | |
| self.betas = ( | |
| torch.linspace(beta_start ** 0.5, beta_end ** 0.5, num_train_timesteps, dtype=torch.float32) ** 2 | |
| ) | |
| elif beta_schedule == "squaredcos_cap_v2": | |
| # Glide cosine schedule | |
| self.betas = betas_for_alpha_bar(num_train_timesteps) | |
| else: | |
| raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}") | |
| self.alphas = 1.0 - self.betas | |
| self.alphas_cumprod = torch.cumprod(self.alphas, dim=0) | |
| # Currently we only support VP-type noise schedule | |
| self.alpha_t = torch.sqrt(self.alphas_cumprod) | |
| self.sigma_t = torch.sqrt(1 - self.alphas_cumprod) | |
| self.lambda_t = torch.log(self.alpha_t) - torch.log(self.sigma_t) | |
| # standard deviation of the initial noise distribution | |
| self.init_noise_sigma = 1.0 | |
| if algorithm_type not in ["data_prediction", "noise_prediction"]: | |
| raise NotImplementedError(f"{algorithm_type} does is not implemented for {self.__class__}") | |
| # setable values | |
| self.num_inference_steps = None | |
| timesteps = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=np.float32)[::-1].copy() | |
| self.timesteps = torch.from_numpy(timesteps) | |
| self.timestep_list = [None] * max(predictor_order, corrector_order - 1) | |
| self.model_outputs = [None] * max(predictor_order, corrector_order - 1) | |
| self.tau_func = tau_func | |
| self.predict_x0 = algorithm_type == "data_prediction" | |
| self.lower_order_nums = 0 | |
| self.last_sample = None | |
| def set_timesteps(self, num_inference_steps: int = None, device: Union[str, torch.device] = None): | |
| """ | |
| Sets the discrete timesteps used for the diffusion chain (to be run before inference). | |
| Args: | |
| num_inference_steps (`int`): | |
| The number of diffusion steps used when generating samples with a pre-trained model. | |
| device (`str` or `torch.device`, *optional*): | |
| The device to which the timesteps should be moved to. If `None`, the timesteps are not moved. | |
| """ | |
| # Clipping the minimum of all lambda(t) for numerical stability. | |
| # This is critical for cosine (squaredcos_cap_v2) noise schedule. | |
| clipped_idx = torch.searchsorted(torch.flip(self.lambda_t, [0]), self.config.lambda_min_clipped) | |
| last_timestep = ((self.config.num_train_timesteps - clipped_idx).numpy()).item() | |
| # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891 | |
| if self.config.timestep_spacing == "linspace": | |
| timesteps = ( | |
| np.linspace(0, last_timestep - 1, num_inference_steps + 1).round()[::-1][:-1].copy().astype(np.int64) | |
| ) | |
| elif self.config.timestep_spacing == "leading": | |
| step_ratio = last_timestep // (num_inference_steps + 1) | |
| # creates integer timesteps by multiplying by ratio | |
| # casting to int to avoid issues when num_inference_step is power of 3 | |
| timesteps = (np.arange(0, num_inference_steps + 1) * step_ratio).round()[::-1][:-1].copy().astype(np.int64) | |
| timesteps += self.config.steps_offset | |
| elif self.config.timestep_spacing == "trailing": | |
| step_ratio = self.config.num_train_timesteps / num_inference_steps | |
| # creates integer timesteps by multiplying by ratio | |
| # casting to int to avoid issues when num_inference_step is power of 3 | |
| timesteps = np.arange(last_timestep, 0, -step_ratio).round().copy().astype(np.int64) | |
| timesteps -= 1 | |
| else: | |
| raise ValueError( | |
| f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'." | |
| ) | |
| sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5) | |
| if self.config.use_karras_sigmas: | |
| log_sigmas = np.log(sigmas) | |
| sigmas = self._convert_to_karras(in_sigmas=sigmas, num_inference_steps=num_inference_steps) | |
| timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]).round() | |
| timesteps = np.flip(timesteps).copy().astype(np.int64) | |
| self.sigmas = torch.from_numpy(sigmas) | |
| # when num_inference_steps == num_train_timesteps, we can end up with | |
| # duplicates in timesteps. | |
| _, unique_indices = np.unique(timesteps, return_index=True) | |
| timesteps = timesteps[np.sort(unique_indices)] | |
| self.timesteps = torch.from_numpy(timesteps).to(device) | |
| self.num_inference_steps = len(timesteps) | |
| self.model_outputs = [ | |
| None, | |
| ] * max(self.config.predictor_order, self.config.corrector_order - 1) | |
| self.lower_order_nums = 0 | |
| self.last_sample = None | |
| # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler._threshold_sample | |
| def _threshold_sample(self, sample: torch.FloatTensor) -> torch.FloatTensor: | |
| """ | |
| "Dynamic thresholding: At each sampling step we set s to a certain percentile absolute pixel value in xt0 (the | |
| prediction of x_0 at timestep t), and if s > 1, then we threshold xt0 to the range [-s, s] and then divide by | |
| s. Dynamic thresholding pushes saturated pixels (those near -1 and 1) inwards, thereby actively preventing | |
| pixels from saturation at each step. We find that dynamic thresholding results in significantly better | |
| photorealism as well as better image-text alignment, especially when using very large guidance weights." | |
| https://arxiv.org/abs/2205.11487 | |
| """ | |
| dtype = sample.dtype | |
| batch_size, channels, height, width = sample.shape | |
| if dtype not in (torch.float32, torch.float64): | |
| sample = sample.float() # upcast for quantile calculation, and clamp not implemented for cpu half | |
| # Flatten sample for doing quantile calculation along each image | |
| sample = sample.reshape(batch_size, channels * height * width) | |
| abs_sample = sample.abs() # "a certain percentile absolute pixel value" | |
| s = torch.quantile(abs_sample, self.config.dynamic_thresholding_ratio, dim=1) | |
| s = torch.clamp( | |
| s, min=1, max=self.config.sample_max_value | |
| ) # When clamped to min=1, equivalent to standard clipping to [-1, 1] | |
| s = s.unsqueeze(1) # (batch_size, 1) because clamp will broadcast along dim=0 | |
| sample = torch.clamp(sample, -s, s) / s # "we threshold xt0 to the range [-s, s] and then divide by s" | |
| sample = sample.reshape(batch_size, channels, height, width) | |
| sample = sample.to(dtype) | |
| return sample | |
| # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t | |
| def _sigma_to_t(self, sigma, log_sigmas): | |
| # get log sigma | |
| log_sigma = np.log(sigma) | |
| # get distribution | |
| dists = log_sigma - log_sigmas[:, np.newaxis] | |
| # get sigmas range | |
| low_idx = np.cumsum((dists >= 0), axis=0).argmax(axis=0).clip(max=log_sigmas.shape[0] - 2) | |
| high_idx = low_idx + 1 | |
| low = log_sigmas[low_idx] | |
| high = log_sigmas[high_idx] | |
| # interpolate sigmas | |
| w = (low - log_sigma) / (low - high) | |
| w = np.clip(w, 0, 1) | |
| # transform interpolation to time range | |
| t = (1 - w) * low_idx + w * high_idx | |
| t = t.reshape(sigma.shape) | |
| return t | |
| # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras | |
| def _convert_to_karras(self, in_sigmas: torch.FloatTensor, num_inference_steps) -> torch.FloatTensor: | |
| """Constructs the noise schedule of Karras et al. (2022).""" | |
| sigma_min: float = in_sigmas[-1].item() | |
| sigma_max: float = in_sigmas[0].item() | |
| rho = 7.0 # 7.0 is the value used in the paper | |
| ramp = np.linspace(0, 1, num_inference_steps) | |
| 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 sigmas | |
| def convert_model_output( | |
| self, model_output: torch.FloatTensor, timestep: int, sample: torch.FloatTensor | |
| ) -> torch.FloatTensor: | |
| """ | |
| Convert the model output to the corresponding type the DPMSolver/DPMSolver++ algorithm needs. DPM-Solver is | |
| designed to discretize an integral of the noise prediction model, and DPM-Solver++ is designed to discretize an | |
| integral of the data prediction model. | |
| <Tip> | |
| The algorithm and model type are decoupled. You can use either DPMSolver or DPMSolver++ for both noise | |
| prediction and data prediction models. | |
| </Tip> | |
| Args: | |
| model_output (`torch.FloatTensor`): | |
| The direct output from the learned diffusion model. | |
| timestep (`int`): | |
| The current discrete timestep in the diffusion chain. | |
| sample (`torch.FloatTensor`): | |
| A current instance of a sample created by the diffusion process. | |
| Returns: | |
| `torch.FloatTensor`: | |
| The converted model output. | |
| """ | |
| # SA-Solver_data_prediction needs to solve an integral of the data prediction model. | |
| if self.config.algorithm_type in ["data_prediction"]: | |
| if self.config.prediction_type == "epsilon": | |
| # SA-Solver only needs the "mean" output. | |
| if self.config.variance_type in ["learned", "learned_range"]: | |
| model_output = model_output[:, :3] | |
| alpha_t, sigma_t = self.alpha_t[timestep], self.sigma_t[timestep] | |
| x0_pred = (sample - sigma_t * model_output) / alpha_t | |
| elif self.config.prediction_type == "sample": | |
| x0_pred = model_output | |
| elif self.config.prediction_type == "v_prediction": | |
| alpha_t, sigma_t = self.alpha_t[timestep], self.sigma_t[timestep] | |
| x0_pred = alpha_t * sample - sigma_t * model_output | |
| else: | |
| raise ValueError( | |
| f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or" | |
| " `v_prediction` for the SASolverScheduler." | |
| ) | |
| if self.config.thresholding: | |
| x0_pred = self._threshold_sample(x0_pred) | |
| return x0_pred | |
| # SA-Solver_noise_prediction needs to solve an integral of the noise prediction model. | |
| elif self.config.algorithm_type in ["noise_prediction"]: | |
| if self.config.prediction_type == "epsilon": | |
| # SA-Solver only needs the "mean" output. | |
| if self.config.variance_type in ["learned", "learned_range"]: | |
| epsilon = model_output[:, :3] | |
| else: | |
| epsilon = model_output | |
| elif self.config.prediction_type == "sample": | |
| alpha_t, sigma_t = self.alpha_t[timestep], self.sigma_t[timestep] | |
| epsilon = (sample - alpha_t * model_output) / sigma_t | |
| elif self.config.prediction_type == "v_prediction": | |
| alpha_t, sigma_t = self.alpha_t[timestep], self.sigma_t[timestep] | |
| epsilon = alpha_t * model_output + sigma_t * sample | |
| else: | |
| raise ValueError( | |
| f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or" | |
| " `v_prediction` for the SASolverScheduler." | |
| ) | |
| if self.config.thresholding: | |
| alpha_t, sigma_t = self.alpha_t[timestep], self.sigma_t[timestep] | |
| x0_pred = (sample - sigma_t * epsilon) / alpha_t | |
| x0_pred = self._threshold_sample(x0_pred) | |
| epsilon = (sample - alpha_t * x0_pred) / sigma_t | |
| return epsilon | |
| def get_coefficients_exponential_negative(self, order, interval_start, interval_end): | |
| """ | |
| Calculate the integral of exp(-x) * x^order dx from interval_start to interval_end | |
| """ | |
| assert order in [0, 1, 2, 3], "order is only supported for 0, 1, 2 and 3" | |
| if order == 0: | |
| return torch.exp(-interval_end) * (torch.exp(interval_end - interval_start) - 1) | |
| elif order == 1: | |
| return torch.exp(-interval_end) * ( | |
| (interval_start + 1) * torch.exp(interval_end - interval_start) - (interval_end + 1)) | |
| elif order == 2: | |
| return torch.exp(-interval_end) * ( | |
| (interval_start ** 2 + 2 * interval_start + 2) * torch.exp(interval_end - interval_start) - ( | |
| interval_end ** 2 + 2 * interval_end + 2)) | |
| elif order == 3: | |
| return torch.exp(-interval_end) * ( | |
| (interval_start ** 3 + 3 * interval_start ** 2 + 6 * interval_start + 6) * torch.exp( | |
| interval_end - interval_start) - (interval_end ** 3 + 3 * interval_end ** 2 + 6 * interval_end + 6)) | |
| def get_coefficients_exponential_positive(self, order, interval_start, interval_end, tau): | |
| """ | |
| Calculate the integral of exp(x(1+tau^2)) * x^order dx from interval_start to interval_end | |
| """ | |
| assert order in [0, 1, 2, 3], "order is only supported for 0, 1, 2 and 3" | |
| # after change of variable(cov) | |
| interval_end_cov = (1 + tau ** 2) * interval_end | |
| interval_start_cov = (1 + tau ** 2) * interval_start | |
| if order == 0: | |
| return torch.exp(interval_end_cov) * (1 - torch.exp(-(interval_end_cov - interval_start_cov))) / ( | |
| (1 + tau ** 2)) | |
| elif order == 1: | |
| return torch.exp(interval_end_cov) * ((interval_end_cov - 1) - (interval_start_cov - 1) * torch.exp( | |
| -(interval_end_cov - interval_start_cov))) / ((1 + tau ** 2) ** 2) | |
| elif order == 2: | |
| return torch.exp(interval_end_cov) * ((interval_end_cov ** 2 - 2 * interval_end_cov + 2) - ( | |
| interval_start_cov ** 2 - 2 * interval_start_cov + 2) * torch.exp( | |
| -(interval_end_cov - interval_start_cov))) / ((1 + tau ** 2) ** 3) | |
| elif order == 3: | |
| return torch.exp(interval_end_cov) * ( | |
| (interval_end_cov ** 3 - 3 * interval_end_cov ** 2 + 6 * interval_end_cov - 6) - ( | |
| interval_start_cov ** 3 - 3 * interval_start_cov ** 2 + 6 * interval_start_cov - 6) * torch.exp( | |
| -(interval_end_cov - interval_start_cov))) / ((1 + tau ** 2) ** 4) | |
| def lagrange_polynomial_coefficient(self, order, lambda_list): | |
| """ | |
| Calculate the coefficient of lagrange polynomial | |
| """ | |
| assert order in [0, 1, 2, 3] | |
| assert order == len(lambda_list) - 1 | |
| if order == 0: | |
| return [[1]] | |
| elif order == 1: | |
| return [[1 / (lambda_list[0] - lambda_list[1]), -lambda_list[1] / (lambda_list[0] - lambda_list[1])], | |
| [1 / (lambda_list[1] - lambda_list[0]), -lambda_list[0] / (lambda_list[1] - lambda_list[0])]] | |
| elif order == 2: | |
| denominator1 = (lambda_list[0] - lambda_list[1]) * (lambda_list[0] - lambda_list[2]) | |
| denominator2 = (lambda_list[1] - lambda_list[0]) * (lambda_list[1] - lambda_list[2]) | |
| denominator3 = (lambda_list[2] - lambda_list[0]) * (lambda_list[2] - lambda_list[1]) | |
| return [[1 / denominator1, | |
| (-lambda_list[1] - lambda_list[2]) / denominator1, | |
| lambda_list[1] * lambda_list[2] / denominator1], | |
| [1 / denominator2, | |
| (-lambda_list[0] - lambda_list[2]) / denominator2, | |
| lambda_list[0] * lambda_list[2] / denominator2], | |
| [1 / denominator3, | |
| (-lambda_list[0] - lambda_list[1]) / denominator3, | |
| lambda_list[0] * lambda_list[1] / denominator3] | |
| ] | |
| elif order == 3: | |
| denominator1 = (lambda_list[0] - lambda_list[1]) * (lambda_list[0] - lambda_list[2]) * ( | |
| lambda_list[0] - lambda_list[3]) | |
| denominator2 = (lambda_list[1] - lambda_list[0]) * (lambda_list[1] - lambda_list[2]) * ( | |
| lambda_list[1] - lambda_list[3]) | |
| denominator3 = (lambda_list[2] - lambda_list[0]) * (lambda_list[2] - lambda_list[1]) * ( | |
| lambda_list[2] - lambda_list[3]) | |
| denominator4 = (lambda_list[3] - lambda_list[0]) * (lambda_list[3] - lambda_list[1]) * ( | |
| lambda_list[3] - lambda_list[2]) | |
| return [[1 / denominator1, | |
| (-lambda_list[1] - lambda_list[2] - lambda_list[3]) / denominator1, | |
| (lambda_list[1] * lambda_list[2] + lambda_list[1] * lambda_list[3] + lambda_list[2] * lambda_list[ | |
| 3]) / denominator1, | |
| (-lambda_list[1] * lambda_list[2] * lambda_list[3]) / denominator1], | |
| [1 / denominator2, | |
| (-lambda_list[0] - lambda_list[2] - lambda_list[3]) / denominator2, | |
| (lambda_list[0] * lambda_list[2] + lambda_list[0] * lambda_list[3] + lambda_list[2] * lambda_list[ | |
| 3]) / denominator2, | |
| (-lambda_list[0] * lambda_list[2] * lambda_list[3]) / denominator2], | |
| [1 / denominator3, | |
| (-lambda_list[0] - lambda_list[1] - lambda_list[3]) / denominator3, | |
| (lambda_list[0] * lambda_list[1] + lambda_list[0] * lambda_list[3] + lambda_list[1] * lambda_list[ | |
| 3]) / denominator3, | |
| (-lambda_list[0] * lambda_list[1] * lambda_list[3]) / denominator3], | |
| [1 / denominator4, | |
| (-lambda_list[0] - lambda_list[1] - lambda_list[2]) / denominator4, | |
| (lambda_list[0] * lambda_list[1] + lambda_list[0] * lambda_list[2] + lambda_list[1] * lambda_list[ | |
| 2]) / denominator4, | |
| (-lambda_list[0] * lambda_list[1] * lambda_list[2]) / denominator4] | |
| ] | |
| def get_coefficients_fn(self, order, interval_start, interval_end, lambda_list, tau): | |
| assert order in [1, 2, 3, 4] | |
| assert order == len(lambda_list), 'the length of lambda list must be equal to the order' | |
| coefficients = [] | |
| lagrange_coefficient = self.lagrange_polynomial_coefficient(order - 1, lambda_list) | |
| for i in range(order): | |
| coefficient = 0 | |
| for j in range(order): | |
| if self.predict_x0: | |
| coefficient += lagrange_coefficient[i][j] * self.get_coefficients_exponential_positive( | |
| order - 1 - j, interval_start, interval_end, tau) | |
| else: | |
| coefficient += lagrange_coefficient[i][j] * self.get_coefficients_exponential_negative( | |
| order - 1 - j, interval_start, interval_end) | |
| coefficients.append(coefficient) | |
| assert len(coefficients) == order, 'the length of coefficients does not match the order' | |
| return coefficients | |
| def stochastic_adams_bashforth_update( | |
| self, | |
| model_output: torch.FloatTensor, | |
| prev_timestep: int, | |
| sample: torch.FloatTensor, | |
| noise: torch.FloatTensor, | |
| order: int, | |
| tau: torch.FloatTensor, | |
| ) -> torch.FloatTensor: | |
| """ | |
| One step for the SA-Predictor. | |
| Args: | |
| model_output (`torch.FloatTensor`): | |
| The direct output from the learned diffusion model at the current timestep. | |
| prev_timestep (`int`): | |
| The previous discrete timestep in the diffusion chain. | |
| sample (`torch.FloatTensor`): | |
| A current instance of a sample created by the diffusion process. | |
| order (`int`): | |
| The order of SA-Predictor at this timestep. | |
| Returns: | |
| `torch.FloatTensor`: | |
| The sample tensor at the previous timestep. | |
| """ | |
| assert noise is not None | |
| timestep_list = self.timestep_list | |
| model_output_list = self.model_outputs | |
| s0, t = self.timestep_list[-1], prev_timestep | |
| lambda_t, lambda_s0 = self.lambda_t[t], self.lambda_t[s0] | |
| alpha_t, alpha_s0 = self.alpha_t[t], self.alpha_t[s0] | |
| sigma_t, sigma_s0 = self.sigma_t[t], self.sigma_t[s0] | |
| gradient_part = torch.zeros_like(sample) | |
| h = lambda_t - lambda_s0 | |
| lambda_list = [] | |
| for i in range(order): | |
| lambda_list.append(self.lambda_t[timestep_list[-(i + 1)]]) | |
| gradient_coefficients = self.get_coefficients_fn(order, lambda_s0, lambda_t, lambda_list, tau) | |
| x = sample | |
| if self.predict_x0: | |
| if order == 2: ## if order = 2 we do a modification that does not influence the convergence order similar to unipc. Note: This is used only for few steps sampling. | |
| # The added term is O(h^3). Empirically we find it will slightly improve the image quality. | |
| # ODE case | |
| # gradient_coefficients[0] += 1.0 * torch.exp(lambda_t) * (h ** 2 / 2 - (h - 1 + torch.exp(-h))) / (ns.marginal_lambda(t_prev_list[-1]) - ns.marginal_lambda(t_prev_list[-2])) | |
| # gradient_coefficients[1] -= 1.0 * torch.exp(lambda_t) * (h ** 2 / 2 - (h - 1 + torch.exp(-h))) / (ns.marginal_lambda(t_prev_list[-1]) - ns.marginal_lambda(t_prev_list[-2])) | |
| gradient_coefficients[0] += 1.0 * torch.exp((1 + tau ** 2) * lambda_t) * ( | |
| h ** 2 / 2 - (h * (1 + tau ** 2) - 1 + torch.exp((1 + tau ** 2) * (-h))) / ( | |
| (1 + tau ** 2) ** 2)) / (self.lambda_t[timestep_list[-1]] - self.lambda_t[ | |
| timestep_list[-2]]) | |
| gradient_coefficients[1] -= 1.0 * torch.exp((1 + tau ** 2) * lambda_t) * ( | |
| h ** 2 / 2 - (h * (1 + tau ** 2) - 1 + torch.exp((1 + tau ** 2) * (-h))) / ( | |
| (1 + tau ** 2) ** 2)) / (self.lambda_t[timestep_list[-1]] - self.lambda_t[ | |
| timestep_list[-2]]) | |
| for i in range(order): | |
| if self.predict_x0: | |
| gradient_part += (1 + tau ** 2) * sigma_t * torch.exp(- tau ** 2 * lambda_t) * gradient_coefficients[ | |
| i] * model_output_list[-(i + 1)] | |
| else: | |
| gradient_part += -(1 + tau ** 2) * alpha_t * gradient_coefficients[i] * model_output_list[-(i + 1)] | |
| if self.predict_x0: | |
| noise_part = sigma_t * torch.sqrt(1 - torch.exp(-2 * tau ** 2 * h)) * noise | |
| else: | |
| noise_part = tau * sigma_t * torch.sqrt(torch.exp(2 * h) - 1) * noise | |
| if self.predict_x0: | |
| x_t = torch.exp(-tau ** 2 * h) * (sigma_t / sigma_s0) * x + gradient_part + noise_part | |
| else: | |
| x_t = (alpha_t / alpha_s0) * x + gradient_part + noise_part | |
| x_t = x_t.to(x.dtype) | |
| return x_t | |
| def stochastic_adams_moulton_update( | |
| self, | |
| this_model_output: torch.FloatTensor, | |
| this_timestep: int, | |
| last_sample: torch.FloatTensor, | |
| last_noise: torch.FloatTensor, | |
| this_sample: torch.FloatTensor, | |
| order: int, | |
| tau: torch.FloatTensor, | |
| ) -> torch.FloatTensor: | |
| """ | |
| One step for the SA-Corrector. | |
| Args: | |
| this_model_output (`torch.FloatTensor`): | |
| The model outputs at `x_t`. | |
| this_timestep (`int`): | |
| The current timestep `t`. | |
| last_sample (`torch.FloatTensor`): | |
| The generated sample before the last predictor `x_{t-1}`. | |
| this_sample (`torch.FloatTensor`): | |
| The generated sample after the last predictor `x_{t}`. | |
| order (`int`): | |
| The order of SA-Corrector at this step. | |
| Returns: | |
| `torch.FloatTensor`: | |
| The corrected sample tensor at the current timestep. | |
| """ | |
| assert last_noise is not None | |
| timestep_list = self.timestep_list | |
| model_output_list = self.model_outputs | |
| s0, t = self.timestep_list[-1], this_timestep | |
| lambda_t, lambda_s0 = self.lambda_t[t], self.lambda_t[s0] | |
| alpha_t, alpha_s0 = self.alpha_t[t], self.alpha_t[s0] | |
| sigma_t, sigma_s0 = self.sigma_t[t], self.sigma_t[s0] | |
| gradient_part = torch.zeros_like(this_sample) | |
| h = lambda_t - lambda_s0 | |
| t_list = timestep_list + [this_timestep] | |
| lambda_list = [] | |
| for i in range(order): | |
| lambda_list.append(self.lambda_t[t_list[-(i + 1)]]) | |
| model_prev_list = model_output_list + [this_model_output] | |
| gradient_coefficients = self.get_coefficients_fn(order, lambda_s0, lambda_t, lambda_list, tau) | |
| x = last_sample | |
| if self.predict_x0: | |
| if order == 2: ## if order = 2 we do a modification that does not influence the convergence order similar to UniPC. Note: This is used only for few steps sampling. | |
| # The added term is O(h^3). Empirically we find it will slightly improve the image quality. | |
| # ODE case | |
| # gradient_coefficients[0] += 1.0 * torch.exp(lambda_t) * (h / 2 - (h - 1 + torch.exp(-h)) / h) | |
| # gradient_coefficients[1] -= 1.0 * torch.exp(lambda_t) * (h / 2 - (h - 1 + torch.exp(-h)) / h) | |
| gradient_coefficients[0] += 1.0 * torch.exp((1 + tau ** 2) * lambda_t) * ( | |
| h / 2 - (h * (1 + tau ** 2) - 1 + torch.exp((1 + tau ** 2) * (-h))) / ( | |
| (1 + tau ** 2) ** 2 * h)) | |
| gradient_coefficients[1] -= 1.0 * torch.exp((1 + tau ** 2) * lambda_t) * ( | |
| h / 2 - (h * (1 + tau ** 2) - 1 + torch.exp((1 + tau ** 2) * (-h))) / ( | |
| (1 + tau ** 2) ** 2 * h)) | |
| for i in range(order): | |
| if self.predict_x0: | |
| gradient_part += (1 + tau ** 2) * sigma_t * torch.exp(- tau ** 2 * lambda_t) * gradient_coefficients[ | |
| i] * model_prev_list[-(i + 1)] | |
| else: | |
| gradient_part += -(1 + tau ** 2) * alpha_t * gradient_coefficients[i] * model_prev_list[-(i + 1)] | |
| if self.predict_x0: | |
| noise_part = sigma_t * torch.sqrt(1 - torch.exp(-2 * tau ** 2 * h)) * last_noise | |
| else: | |
| noise_part = tau * sigma_t * torch.sqrt(torch.exp(2 * h) - 1) * last_noise | |
| if self.predict_x0: | |
| x_t = torch.exp(-tau ** 2 * h) * (sigma_t / sigma_s0) * x + gradient_part + noise_part | |
| else: | |
| x_t = (alpha_t / alpha_s0) * x + gradient_part + noise_part | |
| x_t = x_t.to(x.dtype) | |
| return x_t | |
| def step( | |
| self, | |
| model_output: torch.FloatTensor, | |
| timestep: int, | |
| sample: torch.FloatTensor, | |
| generator=None, | |
| return_dict: bool = True, | |
| ) -> Union[SchedulerOutput, Tuple]: | |
| """ | |
| Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with | |
| the SA-Solver. | |
| Args: | |
| model_output (`torch.FloatTensor`): | |
| The direct output from learned diffusion model. | |
| timestep (`int`): | |
| The current discrete timestep in the diffusion chain. | |
| sample (`torch.FloatTensor`): | |
| A current instance of a sample created by the diffusion process. | |
| generator (`torch.Generator`, *optional*): | |
| A random number generator. | |
| return_dict (`bool`): | |
| Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`. | |
| Returns: | |
| [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`: | |
| If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a | |
| tuple is returned where the first element is the sample tensor. | |
| """ | |
| if self.num_inference_steps is None: | |
| raise ValueError( | |
| "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler" | |
| ) | |
| if isinstance(timestep, torch.Tensor): | |
| timestep = timestep.to(self.timesteps.device) | |
| step_index = (self.timesteps == timestep).nonzero() | |
| if len(step_index) == 0: | |
| step_index = len(self.timesteps) - 1 | |
| else: | |
| step_index = step_index.item() | |
| use_corrector = ( | |
| step_index > 0 and self.last_sample is not None | |
| ) | |
| model_output_convert = self.convert_model_output(model_output, timestep, sample) | |
| if use_corrector: | |
| current_tau = self.tau_func(self.timestep_list[-1]) | |
| sample = self.stochastic_adams_moulton_update( | |
| this_model_output=model_output_convert, | |
| this_timestep=timestep, | |
| last_sample=self.last_sample, | |
| last_noise=self.last_noise, | |
| this_sample=sample, | |
| order=self.this_corrector_order, | |
| tau=current_tau, | |
| ) | |
| prev_timestep = 0 if step_index == len(self.timesteps) - 1 else self.timesteps[step_index + 1] | |
| for i in range(max(self.config.predictor_order, self.config.corrector_order - 1) - 1): | |
| self.model_outputs[i] = self.model_outputs[i + 1] | |
| self.timestep_list[i] = self.timestep_list[i + 1] | |
| self.model_outputs[-1] = model_output_convert | |
| self.timestep_list[-1] = timestep | |
| noise = randn_tensor( | |
| model_output.shape, generator=generator, device=model_output.device, dtype=model_output.dtype | |
| ) | |
| if self.config.lower_order_final: | |
| this_predictor_order = min(self.config.predictor_order, len(self.timesteps) - step_index) | |
| this_corrector_order = min(self.config.corrector_order, len(self.timesteps) - step_index + 1) | |
| else: | |
| this_predictor_order = self.config.predictor_order | |
| this_corrector_order = self.config.corrector_order | |
| self.this_predictor_order = min(this_predictor_order, self.lower_order_nums + 1) # warmup for multistep | |
| self.this_corrector_order = min(this_corrector_order, self.lower_order_nums + 2) # warmup for multistep | |
| assert self.this_predictor_order > 0 | |
| assert self.this_corrector_order > 0 | |
| self.last_sample = sample | |
| self.last_noise = noise | |
| current_tau = self.tau_func(self.timestep_list[-1]) | |
| prev_sample = self.stochastic_adams_bashforth_update( | |
| model_output=model_output_convert, | |
| prev_timestep=prev_timestep, | |
| sample=sample, | |
| noise=noise, | |
| order=self.this_predictor_order, | |
| tau=current_tau, | |
| ) | |
| if self.lower_order_nums < max(self.config.predictor_order, self.config.corrector_order - 1): | |
| self.lower_order_nums += 1 | |
| if not return_dict: | |
| return (prev_sample,) | |
| return SchedulerOutput(prev_sample=prev_sample) | |
| def scale_model_input(self, sample: torch.FloatTensor, *args, **kwargs) -> torch.FloatTensor: | |
| """ | |
| Ensures interchangeability with schedulers that need to scale the denoising model input depending on the | |
| current timestep. | |
| Args: | |
| sample (`torch.FloatTensor`): | |
| The input sample. | |
| Returns: | |
| `torch.FloatTensor`: | |
| A scaled input sample. | |
| """ | |
| return sample | |
| # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.add_noise | |
| def add_noise( | |
| self, | |
| original_samples: torch.FloatTensor, | |
| noise: torch.FloatTensor, | |
| timesteps: torch.IntTensor, | |
| ) -> torch.FloatTensor: | |
| # Make sure alphas_cumprod and timestep have same device and dtype as original_samples | |
| alphas_cumprod = self.alphas_cumprod.to(device=original_samples.device, dtype=original_samples.dtype) | |
| timesteps = timesteps.to(original_samples.device) | |
| sqrt_alpha_prod = alphas_cumprod[timesteps] ** 0.5 | |
| sqrt_alpha_prod = sqrt_alpha_prod.flatten() | |
| while len(sqrt_alpha_prod.shape) < len(original_samples.shape): | |
| sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1) | |
| sqrt_one_minus_alpha_prod = (1 - alphas_cumprod[timesteps]) ** 0.5 | |
| sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten() | |
| while len(sqrt_one_minus_alpha_prod.shape) < len(original_samples.shape): | |
| sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1) | |
| noisy_samples = sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise | |
| return noisy_samples | |
| def __len__(self): | |
| return self.config.num_train_timesteps |