# Copyright (c) 2023 Amphion. # # This source code is licensed under the MIT license found in the # LICENSE file in the root directory of this source tree. import numpy as np import torch import torch.nn.functional as F from torch.distributions import Normal def log_sum_exp(x): """numerically stable log_sum_exp implementation that prevents overflow""" # TF ordering axis = len(x.size()) - 1 m, _ = torch.max(x, dim=axis) m2, _ = torch.max(x, dim=axis, keepdim=True) return m + torch.log(torch.sum(torch.exp(x - m2), dim=axis)) def discretized_mix_logistic_loss( y_hat, y, num_classes=256, log_scale_min=-7.0, reduce=True ): """Discretized mixture of logistic distributions loss Note that it is assumed that input is scaled to [-1, 1]. Args: y_hat (Tensor): Predicted output (B x C x T) y (Tensor): Target (B x T x 1). num_classes (int): Number of classes log_scale_min (float): Log scale minimum value reduce (bool): If True, the losses are averaged or summed for each minibatch. Returns Tensor: loss """ assert y_hat.dim() == 3 assert y_hat.size(1) % 3 == 0 nr_mix = y_hat.size(1) // 3 # (B x T x C) y_hat = y_hat.transpose(1, 2) # unpack parameters. (B, T, num_mixtures) x 3 logit_probs = y_hat[:, :, :nr_mix] means = y_hat[:, :, nr_mix : 2 * nr_mix] log_scales = torch.clamp(y_hat[:, :, 2 * nr_mix : 3 * nr_mix], min=log_scale_min) # B x T x 1 -> B x T x num_mixtures y = y.expand_as(means) centered_y = y - means inv_stdv = torch.exp(-log_scales) plus_in = inv_stdv * (centered_y + 1.0 / (num_classes - 1)) cdf_plus = torch.sigmoid(plus_in) min_in = inv_stdv * (centered_y - 1.0 / (num_classes - 1)) cdf_min = torch.sigmoid(min_in) # log probability for edge case of 0 (before scaling) # equivalent: torch.log(torch.sigmoid(plus_in)) log_cdf_plus = plus_in - F.softplus(plus_in) # log probability for edge case of 255 (before scaling) # equivalent: (1 - torch.sigmoid(min_in)).log() log_one_minus_cdf_min = -F.softplus(min_in) # probability for all other cases cdf_delta = cdf_plus - cdf_min mid_in = inv_stdv * centered_y # log probability in the center of the bin, to be used in extreme cases # (not actually used in our code) log_pdf_mid = mid_in - log_scales - 2.0 * F.softplus(mid_in) # tf equivalent """ log_probs = tf.where(x < -0.999, log_cdf_plus, tf.where(x > 0.999, log_one_minus_cdf_min, tf.where(cdf_delta > 1e-5, tf.log(tf.maximum(cdf_delta, 1e-12)), log_pdf_mid - np.log(127.5)))) """ # TODO: cdf_delta <= 1e-5 actually can happen. How can we choose the value # for num_classes=65536 case? 1e-7? not sure.. inner_inner_cond = (cdf_delta > 1e-5).float() inner_inner_out = inner_inner_cond * torch.log( torch.clamp(cdf_delta, min=1e-12) ) + (1.0 - inner_inner_cond) * (log_pdf_mid - np.log((num_classes - 1) / 2)) inner_cond = (y > 0.999).float() inner_out = ( inner_cond * log_one_minus_cdf_min + (1.0 - inner_cond) * inner_inner_out ) cond = (y < -0.999).float() log_probs = cond * log_cdf_plus + (1.0 - cond) * inner_out log_probs = log_probs + F.log_softmax(logit_probs, -1) if reduce: return -torch.sum(log_sum_exp(log_probs)) else: return -log_sum_exp(log_probs).unsqueeze(-1) def to_one_hot(tensor, n, fill_with=1.0): # we perform one hot encore with respect to the last axis one_hot = torch.FloatTensor(tensor.size() + (n,)).zero_() if tensor.is_cuda: one_hot = one_hot.cuda() one_hot.scatter_(len(tensor.size()), tensor.unsqueeze(-1), fill_with) return one_hot def sample_from_discretized_mix_logistic(y, log_scale_min=-7.0, clamp_log_scale=False): """ Sample from discretized mixture of logistic distributions Args: y (Tensor): B x C x T log_scale_min (float): Log scale minimum value Returns: Tensor: sample in range of [-1, 1]. """ assert y.size(1) % 3 == 0 nr_mix = y.size(1) // 3 # B x T x C y = y.transpose(1, 2) logit_probs = y[:, :, :nr_mix] # sample mixture indicator from softmax temp = logit_probs.data.new(logit_probs.size()).uniform_(1e-5, 1.0 - 1e-5) temp = logit_probs.data - torch.log(-torch.log(temp)) _, argmax = temp.max(dim=-1) # (B, T) -> (B, T, nr_mix) one_hot = to_one_hot(argmax, nr_mix) # select logistic parameters means = torch.sum(y[:, :, nr_mix : 2 * nr_mix] * one_hot, dim=-1) log_scales = torch.sum(y[:, :, 2 * nr_mix : 3 * nr_mix] * one_hot, dim=-1) if clamp_log_scale: log_scales = torch.clamp(log_scales, min=log_scale_min) # sample from logistic & clip to interval # we don't actually round to the nearest 8bit value when sampling u = means.data.new(means.size()).uniform_(1e-5, 1.0 - 1e-5) x = means + torch.exp(log_scales) * (torch.log(u) - torch.log(1.0 - u)) x = torch.clamp(torch.clamp(x, min=-1.0), max=1.0) return x # we can easily define discretized version of the gaussian loss, however, # use continuous version as same as the https://clarinet-demo.github.io/ def mix_gaussian_loss(y_hat, y, log_scale_min=-7.0, reduce=True): """Mixture of continuous gaussian distributions loss Note that it is assumed that input is scaled to [-1, 1]. Args: y_hat (Tensor): Predicted output (B x C x T) y (Tensor): Target (B x T x 1). log_scale_min (float): Log scale minimum value reduce (bool): If True, the losses are averaged or summed for each minibatch. Returns Tensor: loss """ assert y_hat.dim() == 3 C = y_hat.size(1) if C == 2: nr_mix = 1 else: assert y_hat.size(1) % 3 == 0 nr_mix = y_hat.size(1) // 3 # (B x T x C) y_hat = y_hat.transpose(1, 2) # unpack parameters. if C == 2: # special case for C == 2, just for compatibility logit_probs = None means = y_hat[:, :, 0:1] log_scales = torch.clamp(y_hat[:, :, 1:2], min=log_scale_min) else: # (B, T, num_mixtures) x 3 logit_probs = y_hat[:, :, :nr_mix] means = y_hat[:, :, nr_mix : 2 * nr_mix] log_scales = torch.clamp( y_hat[:, :, 2 * nr_mix : 3 * nr_mix], min=log_scale_min ) # B x T x 1 -> B x T x num_mixtures y = y.expand_as(means) centered_y = y - means dist = Normal(loc=0.0, scale=torch.exp(log_scales)) # do we need to add a trick to avoid log(0)? log_probs = dist.log_prob(centered_y) if nr_mix > 1: log_probs = log_probs + F.log_softmax(logit_probs, -1) if reduce: if nr_mix == 1: return -torch.sum(log_probs) else: return -torch.sum(log_sum_exp(log_probs)) else: if nr_mix == 1: return -log_probs else: return -log_sum_exp(log_probs).unsqueeze(-1) def sample_from_mix_gaussian(y, log_scale_min=-7.0): """ Sample from (discretized) mixture of gaussian distributions Args: y (Tensor): B x C x T log_scale_min (float): Log scale minimum value Returns: Tensor: sample in range of [-1, 1]. """ C = y.size(1) if C == 2: nr_mix = 1 else: assert y.size(1) % 3 == 0 nr_mix = y.size(1) // 3 # B x T x C y = y.transpose(1, 2) if C == 2: logit_probs = None else: logit_probs = y[:, :, :nr_mix] if nr_mix > 1: # sample mixture indicator from softmax temp = logit_probs.data.new(logit_probs.size()).uniform_(1e-5, 1.0 - 1e-5) temp = logit_probs.data - torch.log(-torch.log(temp)) _, argmax = temp.max(dim=-1) # (B, T) -> (B, T, nr_mix) one_hot = to_one_hot(argmax, nr_mix) # Select means and log scales means = torch.sum(y[:, :, nr_mix : 2 * nr_mix] * one_hot, dim=-1) log_scales = torch.sum(y[:, :, 2 * nr_mix : 3 * nr_mix] * one_hot, dim=-1) else: if C == 2: means, log_scales = y[:, :, 0], y[:, :, 1] elif C == 3: means, log_scales = y[:, :, 1], y[:, :, 2] else: assert False, "shouldn't happen" scales = torch.exp(log_scales) dist = Normal(loc=means, scale=scales) x = dist.sample() x = torch.clamp(x, min=-1.0, max=1.0) return x