# 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 from ..configuration_utils import ConfigMixin, register_to_config from .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 HeunDiscreteScheduler(SchedulerMixin, ConfigMixin): """ Scheduler with Heun steps for discrete beta schedules. 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` 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). clip_sample (`bool`, defaults to `True`): Clip the predicted sample for numerical stability. clip_sample_range (`float`, defaults to 1.0): The maximum magnitude for sample clipping. Valid only when `clip_sample=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}. 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, clip_sample: Optional[bool] = False, clip_sample_range: float = 1.0, 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, alpha_transform_type="cosine") elif beta_schedule == "exp": self.betas = betas_for_alpha_bar(num_train_timesteps, alpha_transform_type="exp") 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._step_index = None self.sigmas.to("cpu") # to avoid too much CPU/GPU communication 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() @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] sample = sample / ((sigma**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=np.float32)[::-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(np.float32) 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(np.float32) 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.config.use_karras_sigmas: sigmas = self._convert_to_karras(in_sigmas=sigmas, num_inference_steps=self.num_inference_steps) timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in 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) timesteps = torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2)]) self.timesteps = timesteps.to(device=device) # empty dt and derivative self.prev_derivative = None self.dt = None self._step_index = None self.sigmas.to("cpu") # to avoid too much CPU/GPU communication # (YiYi Notes: keep this for now since we are keeping add_noise function which use index_for_timestep) # for exp beta schedules, such as the one for `pipeline_shap_e.py` # we need an index counter self._index_counter = defaultdict(int) # 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(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.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).""" # Hack to make sure that other schedulers which copy this function don't break # TODO: Add this logic to the other schedulers if hasattr(self.config, "sigma_min"): sigma_min = self.config.sigma_min else: sigma_min = None if hasattr(self.config, "sigma_max"): sigma_max = self.config.sigma_max else: sigma_max = None sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item() sigma_max = sigma_max if sigma_max is not None else 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 @property def state_in_first_order(self): return self.dt is None # 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() 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, ) -> 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`): The direct output from learned diffusion model. timestep (`float`): The current discrete timestep in the diffusion chain. sample (`torch.FloatTensor`): A current instance of a sample created by the diffusion process. 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.step_index is None: self._init_step_index(timestep) # (YiYi notes: keep this for now since we are keeping the add_noise method) # advance index counter by 1 timestep_int = timestep.cpu().item() if torch.is_tensor(timestep) else timestep self._index_counter[timestep_int] += 1 if self.state_in_first_order: sigma = self.sigmas[self.step_index] sigma_next = self.sigmas[self.step_index + 1] else: # 2nd order / Heun's method sigma = self.sigmas[self.step_index - 1] sigma_next = self.sigmas[self.step_index] # currently only gamma=0 is supported. This usually works best anyways. # We can support gamma in the future but then need to scale the timestep before # passing it to the model which requires a change in API gamma = 0 sigma_hat = sigma * (gamma + 1) # Note: sigma_hat == sigma for now # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise if self.config.prediction_type == "epsilon": sigma_input = sigma_hat if self.state_in_first_order else sigma_next pred_original_sample = sample - sigma_input * model_output elif self.config.prediction_type == "v_prediction": sigma_input = sigma_hat if self.state_in_first_order else sigma_next pred_original_sample = model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + ( sample / (sigma_input**2 + 1) ) elif self.config.prediction_type == "sample": pred_original_sample = model_output else: raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`" ) if self.config.clip_sample: pred_original_sample = pred_original_sample.clamp( -self.config.clip_sample_range, self.config.clip_sample_range ) if self.state_in_first_order: # 2. Convert to an ODE derivative for 1st order derivative = (sample - pred_original_sample) / sigma_hat # 3. delta timestep dt = sigma_next - sigma_hat # store for 2nd order step self.prev_derivative = derivative self.dt = dt self.sample = sample else: # 2. 2nd order / Heun's method derivative = (sample - pred_original_sample) / sigma_next derivative = (self.prev_derivative + derivative) / 2 # 3. take prev timestep & sample dt = self.dt sample = self.sample # free dt and derivative # Note, this puts the scheduler in "first order mode" self.prev_derivative = None self.dt = None self.sample = None prev_sample = sample + derivative * dt # upon completion increase step index by one self._step_index += 1 if not return_dict: return (prev_sample,) return SchedulerOutput(prev_sample=prev_sample) 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