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vocoder/distribution.py

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+import numpy as np
+import torch
+import torch.nn.functional as F
+
+
+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))
+
+
+# It is adapted from https://github.com/r9y9/wavenet_vocoder/blob/master/wavenet_vocoder/mixture.py
+def discretized_mix_logistic_loss(y_hat, y, num_classes=65536,
+                                  log_scale_min=None, reduce=True):
+    if log_scale_min is None:
+        log_scale_min = float(np.log(1e-14))
+    y_hat = y_hat.permute(0,2,1)
+    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. / (num_classes - 1))
+    cdf_plus = torch.sigmoid(plus_in)
+    min_in = inv_stdv * (centered_y - 1. / (num_classes - 1))
+    cdf_min = torch.sigmoid(min_in)
+
+    # log probability for edge case of 0 (before scaling)
+    # equivalent: torch.log(F.sigmoid(plus_in))
+    log_cdf_plus = plus_in - F.softplus(plus_in)
+
+    # log probability for edge case of 255 (before scaling)
+    # equivalent: (1 - F.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. * 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. - 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. - inner_cond) * inner_inner_out
+    cond = (y < -0.999).float()
+    log_probs = cond * log_cdf_plus + (1. - cond) * inner_out
+
+    log_probs = log_probs + F.log_softmax(logit_probs, -1)
+
+    if reduce:
+        return -torch.mean(log_sum_exp(log_probs))
+    else:
+        return -log_sum_exp(log_probs).unsqueeze(-1)
+
+
+def sample_from_discretized_mix_logistic(y, log_scale_min=None):
+    """
+    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].
+    """
+    if log_scale_min is None:
+        log_scale_min = float(np.log(1e-14))
+    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.clamp(torch.sum(
+        y[:, :, 2 * nr_mix:3 * nr_mix] * one_hot, dim=-1), 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. - u))
+
+    x = torch.clamp(torch.clamp(x, min=-1.), max=1.)
+
+    return x
+
+
+def to_one_hot(tensor, n, fill_with=1.):
+    # 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