# Copyright (c) Meta Platforms, Inc. and affiliates. # All rights reserved. # # This source code is licensed under the license found in the # LICENSE file in the root directory of this source tree. """ Functions for Noise Schedule, defines diffusion process, reverse process and data processor. """ from collections import namedtuple import random import typing as tp import julius import torch TrainingItem = namedtuple("TrainingItem", "noisy noise step") def betas_from_alpha_bar(alpha_bar): alphas = torch.cat([torch.Tensor([alpha_bar[0]]), alpha_bar[1:]/alpha_bar[:-1]]) return 1 - alphas class SampleProcessor(torch.nn.Module): def project_sample(self, x: torch.Tensor): """Project the original sample to the 'space' where the diffusion will happen.""" return x def return_sample(self, z: torch.Tensor): """Project back from diffusion space to the actual sample space.""" return z class MultiBandProcessor(SampleProcessor): """ MultiBand sample processor. The input audio is splitted across frequency bands evenly distributed in mel-scale. Each band will be rescaled to match the power distribution of Gaussian noise in that band, using online metrics computed on the first few samples. Args: n_bands (int): Number of mel-bands to split the signal over. sample_rate (int): Sample rate of the audio. num_samples (int): Number of samples to use to fit the rescaling for each band. The processor won't be stable until it has seen that many samples. power_std (float or list/tensor): The rescaling factor computed to match the power of Gaussian noise in each band is taken to that power, i.e. `1.` means full correction of the energy in each band, and values less than `1` means only partial correction. Can be used to balance the relative importance of low vs. high freq in typical audio signals. """ def __init__(self, n_bands: int = 8, sample_rate: float = 24_000, num_samples: int = 10_000, power_std: tp.Union[float, tp.List[float], torch.Tensor] = 1.): super().__init__() self.n_bands = n_bands self.split_bands = julius.SplitBands(sample_rate, n_bands=n_bands) self.num_samples = num_samples self.power_std = power_std if isinstance(power_std, list): assert len(power_std) == n_bands power_std = torch.tensor(power_std) self.register_buffer('counts', torch.zeros(1)) self.register_buffer('sum_x', torch.zeros(n_bands)) self.register_buffer('sum_x2', torch.zeros(n_bands)) self.register_buffer('sum_target_x2', torch.zeros(n_bands)) self.counts: torch.Tensor self.sum_x: torch.Tensor self.sum_x2: torch.Tensor self.sum_target_x2: torch.Tensor @property def mean(self): mean = self.sum_x / self.counts return mean @property def std(self): std = (self.sum_x2 / self.counts - self.mean**2).clamp(min=0).sqrt() return std @property def target_std(self): target_std = self.sum_target_x2 / self.counts return target_std def project_sample(self, x: torch.Tensor): assert x.dim() == 3 bands = self.split_bands(x) if self.counts.item() < self.num_samples: ref_bands = self.split_bands(torch.randn_like(x)) self.counts += len(x) self.sum_x += bands.mean(dim=(2, 3)).sum(dim=1) self.sum_x2 += bands.pow(2).mean(dim=(2, 3)).sum(dim=1) self.sum_target_x2 += ref_bands.pow(2).mean(dim=(2, 3)).sum(dim=1) rescale = (self.target_std / self.std.clamp(min=1e-12)) ** self.power_std # same output size bands = (bands - self.mean.view(-1, 1, 1, 1)) * rescale.view(-1, 1, 1, 1) return bands.sum(dim=0) def return_sample(self, x: torch.Tensor): assert x.dim() == 3 bands = self.split_bands(x) rescale = (self.std / self.target_std) ** self.power_std bands = bands * rescale.view(-1, 1, 1, 1) + self.mean.view(-1, 1, 1, 1) return bands.sum(dim=0) class NoiseSchedule: """Noise schedule for diffusion. Args: beta_t0 (float): Variance of the first diffusion step. beta_t1 (float): Variance of the last diffusion step. beta_exp (float): Power schedule exponent num_steps (int): Number of diffusion step. variance (str): choice of the sigma value for the denoising eq. Choices: "beta" or "beta_tilde" clip (float): clipping value for the denoising steps rescale (float): rescaling value to avoid vanishing signals unused by default (i.e 1) repartition (str): shape of the schedule only power schedule is supported sample_processor (SampleProcessor): Module that normalize data to match better the gaussian distribution noise_scale (float): Scaling factor for the noise """ def __init__(self, beta_t0: float = 1e-4, beta_t1: float = 0.02, num_steps: int = 1000, variance: str = 'beta', clip: float = 5., rescale: float = 1., device='cuda', beta_exp: float = 1, repartition: str = "power", alpha_sigmoid: dict = {}, n_bands: tp.Optional[int] = None, sample_processor: SampleProcessor = SampleProcessor(), noise_scale: float = 1.0, **kwargs): self.beta_t0 = beta_t0 self.beta_t1 = beta_t1 self.variance = variance self.num_steps = num_steps self.clip = clip self.sample_processor = sample_processor self.rescale = rescale self.n_bands = n_bands self.noise_scale = noise_scale assert n_bands is None if repartition == "power": self.betas = torch.linspace(beta_t0 ** (1 / beta_exp), beta_t1 ** (1 / beta_exp), num_steps, device=device, dtype=torch.float) ** beta_exp else: raise RuntimeError('Not implemented') self.rng = random.Random(1234) def get_beta(self, step: tp.Union[int, torch.Tensor]): if self.n_bands is None: return self.betas[step] else: return self.betas[:, step] # [n_bands, len(step)] def get_initial_noise(self, x: torch.Tensor): if self.n_bands is None: return torch.randn_like(x) return torch.randn((x.size(0), self.n_bands, x.size(2))) def get_alpha_bar(self, step: tp.Optional[tp.Union[int, torch.Tensor]] = None) -> torch.Tensor: """Return 'alpha_bar', either for a given step, or as a tensor with its value for each step.""" if step is None: return (1 - self.betas).cumprod(dim=-1) # works for simgle and multi bands if type(step) is int: return (1 - self.betas[:step + 1]).prod() else: return (1 - self.betas).cumprod(dim=0)[step].view(-1, 1, 1) def get_training_item(self, x: torch.Tensor, tensor_step: bool = False) -> TrainingItem: """Create a noisy data item for diffusion model training: Args: x (torch.Tensor): clean audio data torch.tensor(bs, 1, T) tensor_step (bool): If tensor_step = false, only one step t is sample, the whole batch is diffused to the same step and t is int. If tensor_step = true, t is a tensor of size (x.size(0),) every element of the batch is diffused to a independently sampled. """ step: tp.Union[int, torch.Tensor] if tensor_step: bs = x.size(0) step = torch.randint(0, self.num_steps, size=(bs,), device=x.device) else: step = self.rng.randrange(self.num_steps) alpha_bar = self.get_alpha_bar(step) # [batch_size, n_bands, 1] x = self.sample_processor.project_sample(x) noise = torch.randn_like(x) noisy = (alpha_bar.sqrt() / self.rescale) * x + (1 - alpha_bar).sqrt() * noise * self.noise_scale return TrainingItem(noisy, noise, step) def generate(self, model: torch.nn.Module, initial: tp.Optional[torch.Tensor] = None, condition: tp.Optional[torch.Tensor] = None, return_list: bool = False): """Full ddpm reverse process. Args: model (nn.Module): Diffusion model. initial (tensor): Initial Noise. condition (tensor): Input conditionning Tensor (e.g. encodec compressed representation). return_list (bool): Whether to return the whole process or only the sampled point. """ alpha_bar = self.get_alpha_bar(step=self.num_steps - 1) current = initial iterates = [initial] for step in range(self.num_steps)[::-1]: with torch.no_grad(): estimate = model(current, step, condition=condition).sample alpha = 1 - self.betas[step] previous = (current - (1 - alpha) / (1 - alpha_bar).sqrt() * estimate) / alpha.sqrt() previous_alpha_bar = self.get_alpha_bar(step=step - 1) if step == 0: sigma2 = 0 elif self.variance == 'beta': sigma2 = 1 - alpha elif self.variance == 'beta_tilde': sigma2 = (1 - previous_alpha_bar) / (1 - alpha_bar) * (1 - alpha) elif self.variance == 'none': sigma2 = 0 else: raise ValueError(f'Invalid variance type {self.variance}') if sigma2 > 0: previous += sigma2**0.5 * torch.randn_like(previous) * self.noise_scale if self.clip: previous = previous.clamp(-self.clip, self.clip) current = previous alpha_bar = previous_alpha_bar if step == 0: previous *= self.rescale if return_list: iterates.append(previous.cpu()) if return_list: return iterates else: return self.sample_processor.return_sample(previous) def generate_subsampled(self, model: torch.nn.Module, initial: torch.Tensor, step_list: tp.Optional[list] = None, condition: tp.Optional[torch.Tensor] = None, return_list: bool = False): """Reverse process that only goes through Markov chain states in step_list.""" if step_list is None: step_list = list(range(1000))[::-50] + [0] alpha_bar = self.get_alpha_bar(step=self.num_steps - 1) alpha_bars_subsampled = (1 - self.betas).cumprod(dim=0)[list(reversed(step_list))].cpu() betas_subsampled = betas_from_alpha_bar(alpha_bars_subsampled) current = initial * self.noise_scale iterates = [current] for idx, step in enumerate(step_list[:-1]): with torch.no_grad(): estimate = model(current, step, condition=condition).sample * self.noise_scale alpha = 1 - betas_subsampled[-1 - idx] previous = (current - (1 - alpha) / (1 - alpha_bar).sqrt() * estimate) / alpha.sqrt() previous_alpha_bar = self.get_alpha_bar(step_list[idx + 1]) if step == step_list[-2]: sigma2 = 0 previous_alpha_bar = torch.tensor(1.0) else: sigma2 = (1 - previous_alpha_bar) / (1 - alpha_bar) * (1 - alpha) if sigma2 > 0: previous += sigma2**0.5 * torch.randn_like(previous) * self.noise_scale if self.clip: previous = previous.clamp(-self.clip, self.clip) current = previous alpha_bar = previous_alpha_bar if step == 0: previous *= self.rescale if return_list: iterates.append(previous.cpu()) if return_list: return iterates else: return self.sample_processor.return_sample(previous)