# Copyright 2023 ParaDiGMS authors and The HuggingFace Team. 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. # DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion # and https://github.com/hojonathanho/diffusion import math from dataclasses import dataclass from typing import List, Optional, Tuple, Union import numpy as np import torch from ..configuration_utils import ConfigMixin, register_to_config from ..utils import BaseOutput from ..utils.torch_utils import randn_tensor from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin @dataclass # Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput class DDIMParallelSchedulerOutput(BaseOutput): """ Output class for the scheduler's `step` function output. Args: prev_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images): Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the denoising loop. pred_original_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images): The predicted denoised sample `(x_{0})` based on the model output from the current timestep. `pred_original_sample` can be used to preview progress or for guidance. """ prev_sample: torch.FloatTensor pred_original_sample: Optional[torch.FloatTensor] = None # 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) # Copied from diffusers.schedulers.scheduling_ddim.rescale_zero_terminal_snr def rescale_zero_terminal_snr(betas): """ Rescales betas to have zero terminal SNR Based on https://arxiv.org/pdf/2305.08891.pdf (Algorithm 1) Args: betas (`torch.FloatTensor`): the betas that the scheduler is being initialized with. Returns: `torch.FloatTensor`: rescaled betas with zero terminal SNR """ # Convert betas to alphas_bar_sqrt alphas = 1.0 - betas alphas_cumprod = torch.cumprod(alphas, dim=0) alphas_bar_sqrt = alphas_cumprod.sqrt() # Store old values. alphas_bar_sqrt_0 = alphas_bar_sqrt[0].clone() alphas_bar_sqrt_T = alphas_bar_sqrt[-1].clone() # Shift so the last timestep is zero. alphas_bar_sqrt -= alphas_bar_sqrt_T # Scale so the first timestep is back to the old value. alphas_bar_sqrt *= alphas_bar_sqrt_0 / (alphas_bar_sqrt_0 - alphas_bar_sqrt_T) # Convert alphas_bar_sqrt to betas alphas_bar = alphas_bar_sqrt**2 # Revert sqrt alphas = alphas_bar[1:] / alphas_bar[:-1] # Revert cumprod alphas = torch.cat([alphas_bar[0:1], alphas]) betas = 1 - alphas return betas class DDIMParallelScheduler(SchedulerMixin, ConfigMixin): """ Denoising diffusion implicit models is a scheduler that extends the denoising procedure introduced in denoising diffusion probabilistic models (DDPMs) with non-Markovian guidance. [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__` function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`. [`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and [`~SchedulerMixin.from_pretrained`] functions. For more details, see the original paper: https://arxiv.org/abs/2010.02502 Args: num_train_timesteps (`int`): number of diffusion steps used to train the model. beta_start (`float`): the starting `beta` value of inference. beta_end (`float`): the final `beta` value. beta_schedule (`str`): 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): option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc. clip_sample (`bool`, default `True`): option to clip predicted sample for numerical stability. clip_sample_range (`float`, default `1.0`): the maximum magnitude for sample clipping. Valid only when `clip_sample=True`. set_alpha_to_one (`bool`, default `True`): each diffusion step uses the value of alphas product at that step and at the previous one. For the final step there is no previous alpha. When this option is `True` the previous alpha product is fixed to `1`, otherwise it uses the value of alpha at step 0. steps_offset (`int`, default `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, as done in stable diffusion. prediction_type (`str`, default `epsilon`, optional): prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion process), `sample` (directly predicting the noisy sample`) or `v_prediction` (see section 2.4 https://imagen.research.google/video/paper.pdf) thresholding (`bool`, default `False`): whether to use the "dynamic thresholding" method (introduced by Imagen, https://arxiv.org/abs/2205.11487). Note that the thresholding method is unsuitable for latent-space diffusion models (such as stable-diffusion). dynamic_thresholding_ratio (`float`, default `0.995`): the ratio for the dynamic thresholding method. Default is `0.995`, the same as Imagen (https://arxiv.org/abs/2205.11487). Valid only when `thresholding=True`. sample_max_value (`float`, default `1.0`): the threshold value for dynamic thresholding. Valid only when `thresholding=True`. timestep_spacing (`str`, default `"leading"`): The way the timesteps should be scaled. Refer to Table 2. of [Common Diffusion Noise Schedules and Sample Steps are Flawed](https://arxiv.org/abs/2305.08891) for more information. rescale_betas_zero_snr (`bool`, default `False`): whether to rescale the betas to have zero terminal SNR (proposed by https://arxiv.org/pdf/2305.08891.pdf). This can enable the model to generate very bright and dark samples instead of limiting it to samples with medium brightness. Loosely related to [`--offset_noise`](https://github.com/huggingface/diffusers/blob/74fd735eb073eb1d774b1ab4154a0876eb82f055/examples/dreambooth/train_dreambooth.py#L506). """ _compatibles = [e.name for e in KarrasDiffusionSchedulers] order = 1 _is_ode_scheduler = True @register_to_config # Copied from diffusers.schedulers.scheduling_ddim.DDIMScheduler.__init__ 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, clip_sample: bool = True, set_alpha_to_one: bool = True, steps_offset: int = 0, prediction_type: str = "epsilon", thresholding: bool = False, dynamic_thresholding_ratio: float = 0.995, clip_sample_range: float = 1.0, sample_max_value: float = 1.0, timestep_spacing: str = "leading", rescale_betas_zero_snr: bool = False, ): 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__}") # Rescale for zero SNR if rescale_betas_zero_snr: self.betas = rescale_zero_terminal_snr(self.betas) self.alphas = 1.0 - self.betas self.alphas_cumprod = torch.cumprod(self.alphas, dim=0) # At every step in ddim, we are looking into the previous alphas_cumprod # For the final step, there is no previous alphas_cumprod because we are already at 0 # `set_alpha_to_one` decides whether we set this parameter simply to one or # whether we use the final alpha of the "non-previous" one. self.final_alpha_cumprod = torch.tensor(1.0) if set_alpha_to_one else self.alphas_cumprod[0] # standard deviation of the initial noise distribution self.init_noise_sigma = 1.0 # setable values self.num_inference_steps = None self.timesteps = torch.from_numpy(np.arange(0, num_train_timesteps)[::-1].copy().astype(np.int64)) # Copied from diffusers.schedulers.scheduling_ddim.DDIMScheduler.scale_model_input def scale_model_input(self, sample: torch.FloatTensor, timestep: Optional[int] = None) -> 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. """ return sample def _get_variance(self, timestep, prev_timestep=None): if prev_timestep is None: prev_timestep = timestep - self.config.num_train_timesteps // self.num_inference_steps alpha_prod_t = self.alphas_cumprod[timestep] alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod beta_prod_t = 1 - alpha_prod_t beta_prod_t_prev = 1 - alpha_prod_t_prev variance = (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev) return variance def _batch_get_variance(self, t, prev_t): alpha_prod_t = self.alphas_cumprod[t] alpha_prod_t_prev = self.alphas_cumprod[torch.clip(prev_t, min=0)] alpha_prod_t_prev[prev_t < 0] = torch.tensor(1.0) beta_prod_t = 1 - alpha_prod_t beta_prod_t_prev = 1 - alpha_prod_t_prev variance = (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev) return variance # 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, *remaining_dims = 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 * np.prod(remaining_dims)) 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, *remaining_dims) sample = sample.to(dtype) return sample # Copied from diffusers.schedulers.scheduling_ddim.DDIMScheduler.set_timesteps def set_timesteps(self, num_inference_steps: int, 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. """ if num_inference_steps > self.config.num_train_timesteps: raise ValueError( f"`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:" f" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle" f" maximal {self.config.num_train_timesteps} timesteps." ) self.num_inference_steps = num_inference_steps # "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, self.config.num_train_timesteps - 1, num_inference_steps) .round()[::-1] .copy() .astype(np.int64) ) elif self.config.timestep_spacing == "leading": step_ratio = self.config.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.int64) timesteps += self.config.steps_offset elif self.config.timestep_spacing == "trailing": step_ratio = self.config.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.round(np.arange(self.config.num_train_timesteps, 0, -step_ratio)).astype(np.int64) timesteps -= 1 else: raise ValueError( f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'leading' or 'trailing'." ) self.timesteps = torch.from_numpy(timesteps).to(device) def step( self, model_output: torch.FloatTensor, timestep: int, sample: torch.FloatTensor, eta: float = 0.0, use_clipped_model_output: bool = False, generator=None, variance_noise: Optional[torch.FloatTensor] = None, return_dict: bool = True, ) -> Union[DDIMParallelSchedulerOutput, Tuple]: """ Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion process from the learned model outputs (most often the predicted noise). Args: model_output (`torch.FloatTensor`): direct output from learned diffusion model. timestep (`int`): current discrete timestep in the diffusion chain. sample (`torch.FloatTensor`): current instance of sample being created by diffusion process. eta (`float`): weight of noise for added noise in diffusion step. use_clipped_model_output (`bool`): if `True`, compute "corrected" `model_output` from the clipped predicted original sample. Necessary because predicted original sample is clipped to [-1, 1] when `self.config.clip_sample` is `True`. If no clipping has happened, "corrected" `model_output` would coincide with the one provided as input and `use_clipped_model_output` will have not effect. generator: random number generator. variance_noise (`torch.FloatTensor`): instead of generating noise for the variance using `generator`, we can directly provide the noise for the variance itself. This is useful for methods such as CycleDiffusion. (https://arxiv.org/abs/2210.05559) return_dict (`bool`): option for returning tuple rather than DDIMParallelSchedulerOutput class Returns: [`~schedulers.scheduling_utils.DDIMParallelSchedulerOutput`] or `tuple`: [`~schedulers.scheduling_utils.DDIMParallelSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When returning a tuple, 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" ) # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf # Ideally, read DDIM paper in-detail understanding # Notation ( -> # - pred_noise_t -> e_theta(x_t, t) # - pred_original_sample -> f_theta(x_t, t) or x_0 # - std_dev_t -> sigma_t # - eta -> η # - pred_sample_direction -> "direction pointing to x_t" # - pred_prev_sample -> "x_t-1" # 1. get previous step value (=t-1) prev_timestep = timestep - self.config.num_train_timesteps // self.num_inference_steps # 2. compute alphas, betas alpha_prod_t = self.alphas_cumprod[timestep] alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod beta_prod_t = 1 - alpha_prod_t # 3. compute predicted original sample from predicted noise also called # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf if self.config.prediction_type == "epsilon": pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5) pred_epsilon = model_output elif self.config.prediction_type == "sample": pred_original_sample = model_output pred_epsilon = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5) elif self.config.prediction_type == "v_prediction": pred_original_sample = (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output pred_epsilon = (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample else: raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or" " `v_prediction`" ) # 4. Clip or threshold "predicted x_0" if self.config.thresholding: pred_original_sample = self._threshold_sample(pred_original_sample) elif self.config.clip_sample: pred_original_sample = pred_original_sample.clamp( -self.config.clip_sample_range, self.config.clip_sample_range ) # 5. compute variance: "sigma_t(η)" -> see formula (16) # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1) variance = self._get_variance(timestep, prev_timestep) std_dev_t = eta * variance ** (0.5) if use_clipped_model_output: # the pred_epsilon is always re-derived from the clipped x_0 in Glide pred_epsilon = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5) # 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf pred_sample_direction = (1 - alpha_prod_t_prev - std_dev_t**2) ** (0.5) * pred_epsilon # 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf prev_sample = alpha_prod_t_prev ** (0.5) * pred_original_sample + pred_sample_direction if eta > 0: if variance_noise is not None and generator is not None: raise ValueError( "Cannot pass both generator and variance_noise. Please make sure that either `generator` or" " `variance_noise` stays `None`." ) if variance_noise is None: variance_noise = randn_tensor( model_output.shape, generator=generator, device=model_output.device, dtype=model_output.dtype ) variance = std_dev_t * variance_noise prev_sample = prev_sample + variance if not return_dict: return (prev_sample,) return DDIMParallelSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_sample) def batch_step_no_noise( self, model_output: torch.FloatTensor, timesteps: List[int], sample: torch.FloatTensor, eta: float = 0.0, use_clipped_model_output: bool = False, ) -> torch.FloatTensor: """ Batched version of the `step` function, to be able to reverse the SDE for multiple samples/timesteps at once. Also, does not add any noise to the predicted sample, which is necessary for parallel sampling where the noise is pre-sampled by the pipeline. Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion process from the learned model outputs (most often the predicted noise). Args: model_output (`torch.FloatTensor`): direct output from learned diffusion model. timesteps (`List[int]`): current discrete timesteps in the diffusion chain. This is now a list of integers. sample (`torch.FloatTensor`): current instance of sample being created by diffusion process. eta (`float`): weight of noise for added noise in diffusion step. use_clipped_model_output (`bool`): if `True`, compute "corrected" `model_output` from the clipped predicted original sample. Necessary because predicted original sample is clipped to [-1, 1] when `self.config.clip_sample` is `True`. If no clipping has happened, "corrected" `model_output` would coincide with the one provided as input and `use_clipped_model_output` will have not effect. Returns: `torch.FloatTensor`: sample tensor at previous timestep. """ 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" ) assert eta == 0.0 # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf # Ideally, read DDIM paper in-detail understanding # Notation ( -> # - pred_noise_t -> e_theta(x_t, t) # - pred_original_sample -> f_theta(x_t, t) or x_0 # - std_dev_t -> sigma_t # - eta -> η # - pred_sample_direction -> "direction pointing to x_t" # - pred_prev_sample -> "x_t-1" # 1. get previous step value (=t-1) t = timesteps prev_t = t - self.config.num_train_timesteps // self.num_inference_steps t = t.view(-1, *([1] * (model_output.ndim - 1))) prev_t = prev_t.view(-1, *([1] * (model_output.ndim - 1))) # 1. compute alphas, betas self.alphas_cumprod = self.alphas_cumprod.to(model_output.device) self.final_alpha_cumprod = self.final_alpha_cumprod.to(model_output.device) alpha_prod_t = self.alphas_cumprod[t] alpha_prod_t_prev = self.alphas_cumprod[torch.clip(prev_t, min=0)] alpha_prod_t_prev[prev_t < 0] = torch.tensor(1.0) beta_prod_t = 1 - alpha_prod_t # 3. compute predicted original sample from predicted noise also called # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf if self.config.prediction_type == "epsilon": pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5) pred_epsilon = model_output elif self.config.prediction_type == "sample": pred_original_sample = model_output pred_epsilon = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5) elif self.config.prediction_type == "v_prediction": pred_original_sample = (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output pred_epsilon = (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample else: raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or" " `v_prediction`" ) # 4. Clip or threshold "predicted x_0" if self.config.thresholding: pred_original_sample = self._threshold_sample(pred_original_sample) elif self.config.clip_sample: pred_original_sample = pred_original_sample.clamp( -self.config.clip_sample_range, self.config.clip_sample_range ) # 5. compute variance: "sigma_t(η)" -> see formula (16) # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1) variance = self._batch_get_variance(t, prev_t).to(model_output.device).view(*alpha_prod_t_prev.shape) std_dev_t = eta * variance ** (0.5) if use_clipped_model_output: # the pred_epsilon is always re-derived from the clipped x_0 in Glide pred_epsilon = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5) # 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf pred_sample_direction = (1 - alpha_prod_t_prev - std_dev_t**2) ** (0.5) * pred_epsilon # 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf prev_sample = alpha_prod_t_prev ** (0.5) * pred_original_sample + pred_sample_direction return prev_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 # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.get_velocity def get_velocity( self, sample: torch.FloatTensor, noise: torch.FloatTensor, timesteps: torch.IntTensor ) -> torch.FloatTensor: # Make sure alphas_cumprod and timestep have same device and dtype as sample alphas_cumprod = self.alphas_cumprod.to(device=sample.device, dtype=sample.dtype) timesteps = timesteps.to(sample.device) sqrt_alpha_prod = alphas_cumprod[timesteps] ** 0.5 sqrt_alpha_prod = sqrt_alpha_prod.flatten() while len(sqrt_alpha_prod.shape) < len(sample.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(sample.shape): sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1) velocity = sqrt_alpha_prod * noise - sqrt_one_minus_alpha_prod * sample return velocity def __len__(self): return self.config.num_train_timesteps