# Copyright 2023 Katherine Crowson, The HuggingFace Team and hlky. All rights reserved. # # 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. import math from collections import defaultdict from typing import List, Optional, Tuple, Union import numpy as np import torch import torchsde from ..configuration_utils import ConfigMixin, register_to_config from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput class BatchedBrownianTree: """A wrapper around torchsde.BrownianTree that enables batches of entropy.""" def __init__(self, x, t0, t1, seed=None, **kwargs): t0, t1, self.sign = self.sort(t0, t1) w0 = kwargs.get("w0", torch.zeros_like(x)) if seed is None: seed = torch.randint(0, 2**63 - 1, []).item() self.batched = True try: assert len(seed) == x.shape[0] w0 = w0[0] except TypeError: seed = [seed] self.batched = False self.trees = [torchsde.BrownianTree(t0, w0, t1, entropy=s, **kwargs) for s in seed] @staticmethod def sort(a, b): return (a, b, 1) if a < b else (b, a, -1) def __call__(self, t0, t1): t0, t1, sign = self.sort(t0, t1) w = torch.stack([tree(t0, t1) for tree in self.trees]) * (self.sign * sign) return w if self.batched else w[0] class BrownianTreeNoiseSampler: """A noise sampler backed by a torchsde.BrownianTree. Args: x (Tensor): The tensor whose shape, device and dtype to use to generate random samples. sigma_min (float): The low end of the valid interval. sigma_max (float): The high end of the valid interval. seed (int or List[int]): The random seed. If a list of seeds is supplied instead of a single integer, then the noise sampler will use one BrownianTree per batch item, each with its own seed. transform (callable): A function that maps sigma to the sampler's internal timestep. """ def __init__(self, x, sigma_min, sigma_max, seed=None, transform=lambda x: x): self.transform = transform t0, t1 = self.transform(torch.as_tensor(sigma_min)), self.transform(torch.as_tensor(sigma_max)) self.tree = BatchedBrownianTree(x, t0, t1, seed) def __call__(self, sigma, sigma_next): t0, t1 = self.transform(torch.as_tensor(sigma)), self.transform(torch.as_tensor(sigma_next)) return self.tree(t0, t1) / (t1 - t0).abs().sqrt() # 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 DPMSolverSDEScheduler(SchedulerMixin, ConfigMixin): """ DPMSolverSDEScheduler implements the stochastic sampler from the [Elucidating the Design Space of Diffusion-Based Generative Models](https://huggingface.co/papers/2206.00364) paper. 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 0.00085): The starting `beta` value of inference. beta_end (`float`, defaults to 0.012): 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` or `scaled_linear`. trained_betas (`np.ndarray`, *optional*): Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`. 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). 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}. noise_sampler_seed (`int`, *optional*, defaults to `None`): The random seed to use for the noise sampler. If `None`, a random seed is generated. 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 = 2 @register_to_config def __init__( self, num_train_timesteps: int = 1000, beta_start: float = 0.00085, # sensible defaults beta_end: float = 0.012, beta_schedule: str = "linear", trained_betas: Optional[Union[np.ndarray, List[float]]] = None, prediction_type: str = "epsilon", use_karras_sigmas: Optional[bool] = False, noise_sampler_seed: Optional[int] = 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) # set all values self.set_timesteps(num_train_timesteps, None, num_train_timesteps) self.use_karras_sigmas = use_karras_sigmas self.noise_sampler = None self.noise_sampler_seed = noise_sampler_seed self._step_index = None self.sigmas.to("cpu") # to avoid too much CPU/GPU communication # Copied from diffusers.schedulers.scheduling_heun_discrete.HeunDiscreteScheduler.index_for_timestep def index_for_timestep(self, timestep, schedule_timesteps=None): if schedule_timesteps is None: schedule_timesteps = self.timesteps indices = (schedule_timesteps == timestep).nonzero() # The sigma index that is taken for the **very** first `step` # is always the second index (or the last index if there is only 1) # This way we can ensure we don't accidentally skip a sigma in # case we start in the middle of the denoising schedule (e.g. for image-to-image) if len(self._index_counter) == 0: pos = 1 if len(indices) > 1 else 0 else: timestep_int = timestep.cpu().item() if torch.is_tensor(timestep) else timestep pos = self._index_counter[timestep_int] return indices[pos].item() # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._init_step_index def _init_step_index(self, timestep): if isinstance(timestep, torch.Tensor): timestep = timestep.to(self.timesteps.device) index_candidates = (self.timesteps == timestep).nonzero() # The sigma index that is taken for the **very** first `step` # is always the second index (or the last index if there is only 1) # This way we can ensure we don't accidentally skip a sigma in # case we start in the middle of the denoising schedule (e.g. for image-to-image) if len(index_candidates) > 1: step_index = index_candidates[1] else: step_index = index_candidates[0] self._step_index = step_index.item() @property def init_noise_sigma(self): # standard deviation of the initial noise distribution if self.config.timestep_spacing in ["linspace", "trailing"]: return self.sigmas.max() return (self.sigmas.max() ** 2 + 1) ** 0.5 @property def step_index(self): """ The index counter for current timestep. It will increae 1 after each scheduler step. """ return self._step_index def scale_model_input( self, sample: torch.FloatTensor, timestep: Union[float, torch.FloatTensor], ) -> 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. timestep (`int`, *optional*): The current timestep in the diffusion chain. Returns: `torch.FloatTensor`: A scaled input sample. """ if self.step_index is None: self._init_step_index(timestep) sigma = self.sigmas[self.step_index] sigma_input = sigma if self.state_in_first_order else self.mid_point_sigma sample = sample / ((sigma_input**2 + 1) ** 0.5) return sample def set_timesteps( self, num_inference_steps: int, device: Union[str, torch.device] = None, num_train_timesteps: Optional[int] = 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. """ self.num_inference_steps = num_inference_steps num_train_timesteps = num_train_timesteps or self.config.num_train_timesteps # "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, num_train_timesteps - 1, num_inference_steps, dtype=float)[::-1].copy() elif self.config.timestep_spacing == "leading": step_ratio = num_train_timesteps // self.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(0, num_inference_steps) * step_ratio).round()[::-1].copy().astype(float) timesteps += self.config.steps_offset elif self.config.timestep_spacing == "trailing": step_ratio = num_train_timesteps / self.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(num_train_timesteps, 0, -step_ratio)).round().copy().astype(float) 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) log_sigmas = np.log(sigmas) sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas) if self.use_karras_sigmas: sigmas = self._convert_to_karras(in_sigmas=sigmas) timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]) second_order_timesteps = self._second_order_timesteps(sigmas, log_sigmas) sigmas = np.concatenate([sigmas, [0.0]]).astype(np.float32) sigmas = torch.from_numpy(sigmas).to(device=device) self.sigmas = torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2), sigmas[-1:]]) timesteps = torch.from_numpy(timesteps) second_order_timesteps = torch.from_numpy(second_order_timesteps) timesteps = torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2)]) timesteps[1::2] = second_order_timesteps if str(device).startswith("mps"): # mps does not support float64 self.timesteps = timesteps.to(device, dtype=torch.float32) else: self.timesteps = timesteps.to(device=device) # empty first order variables self.sample = None self.mid_point_sigma = None self._step_index = None self.sigmas.to("cpu") # to avoid too much CPU/GPU communication self.noise_sampler = None # for exp beta schedules, such as the one for `pipeline_shap_e.py` # we need an index counter self._index_counter = defaultdict(int) def _second_order_timesteps(self, sigmas, log_sigmas): def sigma_fn(_t): return np.exp(-_t) def t_fn(_sigma): return -np.log(_sigma) midpoint_ratio = 0.5 t = t_fn(sigmas) delta_time = np.diff(t) t_proposed = t[:-1] + delta_time * midpoint_ratio sig_proposed = sigma_fn(t_proposed) timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sig_proposed]) return timesteps # copied from diffusers.schedulers.scheduling_euler_discrete._sigma_to_t def _sigma_to_t(self, sigma, log_sigmas): # get log sigma log_sigma = np.log(np.maximum(sigma, 1e-10)) # 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._convert_to_karras def _convert_to_karras(self, in_sigmas: torch.FloatTensor) -> 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, self.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 @property def state_in_first_order(self): return self.sample is None def step( self, model_output: Union[torch.FloatTensor, np.ndarray], timestep: Union[float, torch.FloatTensor], sample: Union[torch.FloatTensor, np.ndarray], return_dict: bool = True, s_noise: float = 1.0, ) -> Union[SchedulerOutput, Tuple]: """ Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion process from the learned model outputs (most often the predicted noise). Args: model_output (`torch.FloatTensor` or `np.ndarray`): The direct output from learned diffusion model. timestep (`float` or `torch.FloatTensor`): The current discrete timestep in the diffusion chain. sample (`torch.FloatTensor` or `np.ndarray`): A current instance of a sample created by the diffusion process. return_dict (`bool`, *optional*, defaults to `True`): Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or tuple. s_noise (`float`, *optional*, defaults to 1.0): Scaling factor for noise added to the sample. 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.step_index is None: self._init_step_index(timestep) # advance index counter by 1 timestep_int = timestep.cpu().item() if torch.is_tensor(timestep) else timestep self._index_counter[timestep_int] += 1 # Create a noise sampler if it hasn't been created yet if self.noise_sampler is None: min_sigma, max_sigma = self.sigmas[self.sigmas > 0].min(), self.sigmas.max() self.noise_sampler = BrownianTreeNoiseSampler(sample, min_sigma, max_sigma, self.noise_sampler_seed) # Define functions to compute sigma and t from each other def sigma_fn(_t: torch.FloatTensor) -> torch.FloatTensor: return _t.neg().exp() def t_fn(_sigma: torch.FloatTensor) -> torch.FloatTensor: return _sigma.log().neg() if self.state_in_first_order: sigma = self.sigmas[self.step_index] sigma_next = self.sigmas[self.step_index + 1] else: # 2nd order sigma = self.sigmas[self.step_index - 1] sigma_next = self.sigmas[self.step_index] # Set the midpoint and step size for the current step midpoint_ratio = 0.5 t, t_next = t_fn(sigma), t_fn(sigma_next) delta_time = t_next - t t_proposed = t + delta_time * midpoint_ratio # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise if self.config.prediction_type == "epsilon": sigma_input = sigma if self.state_in_first_order else sigma_fn(t_proposed) pred_original_sample = sample - sigma_input * model_output elif self.config.prediction_type == "v_prediction": sigma_input = sigma if self.state_in_first_order else sigma_fn(t_proposed) pred_original_sample = model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + ( sample / (sigma_input**2 + 1) ) elif self.config.prediction_type == "sample": raise NotImplementedError("prediction_type not implemented yet: sample") else: raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`" ) if sigma_next == 0: derivative = (sample - pred_original_sample) / sigma dt = sigma_next - sigma prev_sample = sample + derivative * dt else: if self.state_in_first_order: t_next = t_proposed else: sample = self.sample sigma_from = sigma_fn(t) sigma_to = sigma_fn(t_next) sigma_up = min(sigma_to, (sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5) sigma_down = (sigma_to**2 - sigma_up**2) ** 0.5 ancestral_t = t_fn(sigma_down) prev_sample = (sigma_fn(ancestral_t) / sigma_fn(t)) * sample - ( t - ancestral_t ).expm1() * pred_original_sample prev_sample = prev_sample + self.noise_sampler(sigma_fn(t), sigma_fn(t_next)) * s_noise * sigma_up if self.state_in_first_order: # store for 2nd order step self.sample = sample self.mid_point_sigma = sigma_fn(t_next) else: # free for "first order mode" self.sample = None self.mid_point_sigma = None # upon completion increase step index by one self._step_index += 1 if not return_dict: return (prev_sample,) return SchedulerOutput(prev_sample=prev_sample) # Copied from diffusers.schedulers.scheduling_heun_discrete.HeunDiscreteScheduler.add_noise def add_noise( self, original_samples: torch.FloatTensor, noise: torch.FloatTensor, timesteps: torch.FloatTensor, ) -> torch.FloatTensor: # Make sure sigmas and timesteps have the same device and dtype as original_samples sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype) if original_samples.device.type == "mps" and torch.is_floating_point(timesteps): # mps does not support float64 schedule_timesteps = self.timesteps.to(original_samples.device, dtype=torch.float32) timesteps = timesteps.to(original_samples.device, dtype=torch.float32) else: schedule_timesteps = self.timesteps.to(original_samples.device) timesteps = timesteps.to(original_samples.device) step_indices = [self.index_for_timestep(t, schedule_timesteps) for t in timesteps] sigma = sigmas[step_indices].flatten() while len(sigma.shape) < len(original_samples.shape): sigma = sigma.unsqueeze(-1) noisy_samples = original_samples + noise * sigma return noisy_samples def __len__(self): return self.config.num_train_timesteps