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# ---------------------------------------------------------------
# Copyright (c) 2021, NVIDIA CORPORATION. All rights reserved.
#
# This work is licensed under the NVIDIA Source Code License
# for LSGM. To view a copy of this license, see the LICENSE file.
# ---------------------------------------------------------------
import torch
import torch.nn.functional as F
from torch.distributions.bernoulli import Bernoulli as Bern
import numpy as np
from pdb import set_trace as st
# from util import utils
from .continuous_diffusion_utils import view4D
@torch.jit.script
def sample_normal_jit(mu, sigma):
rho = mu.mul(0).normal_()
z = rho.mul_(sigma).add_(mu)
return z, rho
@torch.jit.script
def log_p_standard_normal(samples):
log_p = - 0.5 * torch.square(samples) - 0.9189385332 # 0.5 * np.log(2 * np.pi)
return log_p
def log_p_var_normal(samples, var):
log_p = - 0.5 * torch.square(samples) / var - 0.5 * np.log(var) - 0.9189385332 # 0.5 * np.log(2 * np.pi)
return log_p
def one_hot(indices, depth, dim):
indices = indices.unsqueeze(dim)
size = list(indices.size())
size[dim] = depth
y_onehot = torch.zeros(size).cuda()
y_onehot.zero_()
y_onehot.scatter_(dim, indices, 1)
return y_onehot
# TODO: merge this with the next class
class PixelNormal(object):
def __init__(self, param, fixed_log_scales=None):
size = param.size()
C = size[1]
if fixed_log_scales is None:
self.num_c = C // 2
self.means = param[:, :self.num_c, :, :] # B, 1 or 3, H, W
self.log_scales = torch.clamp(param[:, self.num_c:, :, :], min=-7.0) # B, 1 or 3, H, W
raise NotImplementedError
else:
self.num_c = C
self.means = param # B, 1 or 3, H, W
self.log_scales = view4D(fixed_log_scales, size) # B, 1 or 3, H, W
def get_params(self):
return self.means, self.log_scales, self.num_c
def log_prob(self, samples):
B, C, H, W = samples.size()
assert C == self.num_c
log_probs = -0.5 * torch.square(self.means - samples) * torch.exp(-2.0 * self.log_scales) - self.log_scales - 0.9189385332 # -0.5*log(2*pi)
return log_probs
def sample(self, t=1.):
z, rho = sample_normal_jit(self.means, torch.exp(self.log_scales)*t) # B, 3, H, W
return z
def log_prob_discrete(self, samples):
"""
Calculates discrete pixel probabilities.
"""
# samples should be in [-1, 1] already
B, C, H, W = samples.size()
assert C == self.num_c
centered = samples - self.means
inv_stdv = torch.exp(- self.log_scales)
plus_in = inv_stdv * (centered + 1. / 255.)
cdf_plus = torch.distributions.Normal(0, 1).cdf(plus_in)
min_in = inv_stdv * (centered - 1. / 255.)
cdf_min = torch.distributions.Normal(0, 1).cdf(min_in)
log_cdf_plus = torch.log(torch.clamp(cdf_plus, min=1e-12))
log_one_minus_cdf_min = torch.log(torch.clamp(1. - cdf_min, min=1e-12))
cdf_delta = cdf_plus - cdf_min
log_probs = torch.where(samples < -0.999, log_cdf_plus, torch.where(samples > 0.999, log_one_minus_cdf_min,
torch.log(torch.clamp(cdf_delta, min=1e-12))))
assert log_probs.size() == samples.size()
return log_probs
def mean(self):
return self.means
class Normal:
def __init__(self, mu, log_sigma):
self.mu = mu
self.log_sigma = log_sigma
self.sigma = torch.exp(log_sigma)
def sample(self, t=1.):
return sample_normal_jit(self.mu, self.sigma * t)
def sample_given_rho(self, rho):
return rho * self.sigma + self.mu
def log_p(self, samples):
normalized_samples = (samples - self.mu) / self.sigma
log_p = - 0.5 * normalized_samples * normalized_samples - 0.5 * np.log(2 * np.pi) - self.log_sigma
return log_p
def kl(self, normal_dist):
term1 = (self.mu - normal_dist.mu) / normal_dist.sigma
term2 = self.sigma / normal_dist.sigma
return 0.5 * (term1 * term1 + term2 * term2) - 0.5 - torch.log(self.log_sigma) + normal_dist.log_sigma
def mean(self):
return self.mu
class Bernoulli:
def __init__(self, logits):
self.dist = Bern(logits=logits)
def log_p(self, samples):
# convert samples to {0, 1}
samples = (samples + 1.) / 2
return self.dist.log_prob(samples)
def mean(self):
# map the mean to [-1, 1]
return 2 * self.dist.mean - 1.
class DiscLogistic:
def __init__(self, param):
B, C, H, W = param.size()
self.num_c = C // 2
self.means = param[:, :self.num_c, :, :] # B, 3, H, W
self.log_scales = torch.clamp(param[:, self.num_c:, :, :], min=-7.0) # B, 3, H, W
def log_p(self, samples):
assert torch.max(samples) <= 1.0 and torch.min(samples) >= -1.0
B, C, H, W = samples.size()
assert C == self.num_c
centered = samples - self.means # B, 3, H, W
inv_stdv = torch.exp(- self.log_scales)
plus_in = inv_stdv * (centered + 1. / 255.)
cdf_plus = torch.sigmoid(plus_in)
min_in = inv_stdv * (centered - 1. / 255.)
cdf_min = torch.sigmoid(min_in)
log_cdf_plus = plus_in - F.softplus(plus_in)
log_one_minus_cdf_min = - F.softplus(min_in)
cdf_delta = cdf_plus - cdf_min
mid_in = inv_stdv * centered
log_pdf_mid = mid_in - self.log_scales - 2. * F.softplus(mid_in)
log_prob_mid_safe = torch.where(cdf_delta > 1e-5,
torch.log(torch.clamp(cdf_delta, min=1e-10)),
log_pdf_mid - np.log(127.5))
log_probs = torch.where(samples < -0.999, log_cdf_plus, torch.where(samples > 0.999, log_one_minus_cdf_min,
log_prob_mid_safe)) # B, 3, H, W
return log_probs
def sample(self):
u = torch.Tensor(self.means.size()).uniform_(1e-5, 1. - 1e-5).cuda() # B, 3, H, W
x = self.means + torch.exp(self.log_scales) * (torch.log(u) - torch.log(1. - u)) # B, 3, H, W
x = torch.clamp(x, -1, 1.)
return x
def mean(self):
return self.means
class DiscMixLogistic:
def __init__(self, param, num_mix=10, num_bits=8):
B, C, H, W = param.size()
self.num_mix = num_mix
self.logit_probs = param[:, :num_mix, :, :] # B, M, H, W
l = param[:, num_mix:, :, :].view(B, 3, 3 * num_mix, H, W) # B, 3, 3 * M, H, W
self.means = l[:, :, :num_mix, :, :] # B, 3, M, H, W
self.log_scales = torch.clamp(l[:, :, num_mix:2 * num_mix, :, :], min=-7.0) # B, 3, M, H, W
self.coeffs = torch.tanh(l[:, :, 2 * num_mix:3 * num_mix, :, :]) # B, 3, M, H, W
self.max_val = 2. ** num_bits - 1
def log_p(self, samples):
assert torch.max(samples) <= 1.0 and torch.min(samples) >= -1.0
B, C, H, W = samples.size()
assert C == 3, 'only RGB images are considered.'
samples = samples.unsqueeze(4) # B, 3, H , W
samples = samples.expand(-1, -1, -1, -1, self.num_mix).permute(0, 1, 4, 2, 3) # B, 3, M, H, W
mean1 = self.means[:, 0, :, :, :] # B, M, H, W
mean2 = self.means[:, 1, :, :, :] + \
self.coeffs[:, 0, :, :, :] * samples[:, 0, :, :, :] # B, M, H, W
mean3 = self.means[:, 2, :, :, :] + \
self.coeffs[:, 1, :, :, :] * samples[:, 0, :, :, :] + \
self.coeffs[:, 2, :, :, :] * samples[:, 1, :, :, :] # B, M, H, W
mean1 = mean1.unsqueeze(1) # B, 1, M, H, W
mean2 = mean2.unsqueeze(1) # B, 1, M, H, W
mean3 = mean3.unsqueeze(1) # B, 1, M, H, W
means = torch.cat([mean1, mean2, mean3], dim=1) # B, 3, M, H, W
centered = samples - means # B, 3, M, H, W
inv_stdv = torch.exp(- self.log_scales)
plus_in = inv_stdv * (centered + 1. / self.max_val)
cdf_plus = torch.sigmoid(plus_in)
min_in = inv_stdv * (centered - 1. / self.max_val)
cdf_min = torch.sigmoid(min_in)
log_cdf_plus = plus_in - F.softplus(plus_in)
log_one_minus_cdf_min = - F.softplus(min_in)
cdf_delta = cdf_plus - cdf_min
mid_in = inv_stdv * centered
log_pdf_mid = mid_in - self.log_scales - 2. * F.softplus(mid_in)
log_prob_mid_safe = torch.where(cdf_delta > 1e-5,
torch.log(torch.clamp(cdf_delta, min=1e-10)),
log_pdf_mid - np.log(self.max_val / 2))
log_probs = torch.where(samples < -0.999, log_cdf_plus, torch.where(samples > 0.999, log_one_minus_cdf_min,
log_prob_mid_safe)) # B, 3, M, H, W
log_probs = torch.sum(log_probs, 1) + F.log_softmax(self.logit_probs, dim=1) # B, M, H, W
return torch.logsumexp(log_probs, dim=1) # B, H, W
def sample(self, t=1.):
gumbel = -torch.log(- torch.log(torch.Tensor(self.logit_probs.size()).uniform_(1e-5, 1. - 1e-5).cuda())) # B, M, H, W
sel = one_hot(torch.argmax(self.logit_probs / t + gumbel, 1), self.num_mix, dim=1) # B, M, H, W
sel = sel.unsqueeze(1) # B, 1, M, H, W
# select logistic parameters
means = torch.sum(self.means * sel, dim=2) # B, 3, H, W
log_scales = torch.sum(self.log_scales * sel, dim=2) # B, 3, H, W
coeffs = torch.sum(self.coeffs * sel, dim=2) # B, 3, H, W
# cells from logistic & clip to interval
# we don't actually round to the nearest 8bit value when sampling
u = torch.Tensor(means.size()).uniform_(1e-5, 1. - 1e-5).cuda() # B, 3, H, W
x = means + torch.exp(log_scales) * t * (torch.log(u) - torch.log(1. - u)) # B, 3, H, W
x0 = torch.clamp(x[:, 0, :, :], -1, 1.) # B, H, W
x1 = torch.clamp(x[:, 1, :, :] + coeffs[:, 0, :, :] * x0, -1, 1) # B, H, W
x2 = torch.clamp(x[:, 2, :, :] + coeffs[:, 1, :, :] * x0 + coeffs[:, 2, :, :] * x1, -1, 1) # B, H, W
x0 = x0.unsqueeze(1)
x1 = x1.unsqueeze(1)
x2 = x2.unsqueeze(1)
x = torch.cat([x0, x1, x2], 1)
return x
def mean(self):
sel = torch.softmax(self.logit_probs, dim=1) # B, M, H, W
sel = sel.unsqueeze(1) # B, 1, M, H, W
# select logistic parameters
means = torch.sum(self.means * sel, dim=2) # B, 3, H, W
coeffs = torch.sum(self.coeffs * sel, dim=2) # B, 3, H, W
# we don't sample from logistic components, because of the linear dependencies, we use mean
x = means # B, 3, H, W
x0 = torch.clamp(x[:, 0, :, :], -1, 1.) # B, H, W
x1 = torch.clamp(x[:, 1, :, :] + coeffs[:, 0, :, :] * x0, -1, 1) # B, H, W
x2 = torch.clamp(x[:, 2, :, :] + coeffs[:, 1, :, :] * x0 + coeffs[:, 2, :, :] * x1, -1, 1) # B, H, W
x0 = x0.unsqueeze(1)
x1 = x1.unsqueeze(1)
x2 = x2.unsqueeze(1)
x = torch.cat([x0, x1, x2], 1)
return x
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