def corrupt(self, x, stage):
"""Corrupts x to a lower depth version for each stage."""
# Note: we take the _generative process_ order. This is the reverse of the
# diffusion process. However, the transition matrices are defined in the
# order of the diffusion process. So here future is 's' and past 's+1'.
stage_reverse = self.num_stages - 1 - stage
if self.direct_parametrization:
t = jnp.expand_dims(stage_reverse, np.arange(1, len(x.shape)))
# The branch_factor determines at which speed the integers are reduced.
# For example: suppose we have a 16-bit problem and we want to model it
# in two stages, we could pick a branch factor of 256. Then, 16383 // 256
# = 255 for the first corruption and 255 // 256 = 0 for the second
# corruption.
x_past = (x // self.branch_factor**
(t + 1)) * self.branch_factor**(t + 1)
x_future = (x // self.branch_factor**t) * self.branch_factor**t
else:
transition_future = self.cum_matmul_transition_matrices[
stage_reverse]
transition_past = self.cum_matmul_transition_matrices[stage_reverse
+ 1]
# Here we compute the past and future x representations.
x_onehot = util_fns.onehot(x, self.num_input_classes)
x_past_onehot = self.transform_with_matrix(x_onehot,
transition_past)
x_past = jnp.argmax(x_past_onehot, axis=-1)
x_future_onehot = self.transform_with_matrix(
x_onehot, transition_future)
x_future = jnp.argmax(x_future_onehot, axis=-1)
return x_future, x_past
def log_prob_for_x_future_given_past(self, x_future, x_past, net_out,
stage):
"""Computes the log probability of x_future given x_past and net_out.
Args:
x_future: The variable to compute the log probability for.
x_past: The variable to condition on.
net_out: Network output containing the logits.
stage: The stage of the specific datapoint.
Returns:
The elementwise log probabilities of x_future.
"""
batch_size = x_future.shape[0]
if self.direct_parametrization:
logits_per_stage = net_out.reshape(*x_future.shape,
self.num_stages,
self.branch_factor)
# Retrieve the logits for this specific stage.
logits = logits_per_stage[jnp.arange(batch_size), Ellipsis,
stage, :]
log_probs = jax.nn.log_softmax(logits, axis=-1)
t = self.num_stages - 1 - stage
t = jnp.expand_dims(t, np.arange(1, len(x_future.shape)))
x_target = (x_future // self.branch_factor**t) % self.branch_factor
x_target_onehot = util_fns.onehot(x_target, self.branch_factor)
log_prob_future_given_past = jnp.sum(log_probs * x_target_onehot,
axis=-1)
else:
logits = net_out.reshape(*x_future.shape, self.num_output_classes)
log_prob_future_given_past = self.log_prob_vector_future_given_past(
logits, x_past, stage)
x_future_onehot = util_fns.onehot(x_future, self.num_input_classes)
log_prob_future_given_past = jnp.sum(log_prob_future_given_past *
x_future_onehot,
axis=-1)
return log_prob_future_given_past
def sample_categorical_and_log_prob(key, logits):
# If logits already normalized, operation does nothing as is desired.
log_p = jax.nn.log_softmax(logits, axis=-1)
category = sample_categorical(key, logits)
category_onehot = util_fns.onehot(category, num_classes=logits.shape[-1])
log_pcategory = (log_p * category_onehot).sum(axis=-1)
return category, log_pcategory
def prepare_additional_input(self, stage, already_predicted):
new_axes = tuple(range(1, len(already_predicted.shape) - 1))
stage = jnp.expand_dims(stage, axis=new_axes)
stage_onehot = util_fns.onehot(stage, num_classes=self.num_stages)
stage_onehot = jnp.broadcast_to(stage_onehot,
shape=already_predicted.shape[:-1] +
(self.num_stages, ))
add_info = jnp.concatenate([already_predicted, stage_onehot], axis=-1)
return add_info
def sample_from_discretized_mix_logistic_rgb(rng, params, nr_mix):
"""Sample from discretized mix logistic distribution."""
xshape = params.shape[:-1] + (3, )
batchsize, height, width, _ = xshape
# unpack parameters
pi_logits = params[:, :, :, :nr_mix]
remaining_params = params[:, :, :, nr_mix:].reshape(*xshape, nr_mix * 3)
# sample mixture indicator from softmax
rng1, rng2 = jax.random.split(rng)
mixture_idcs = sample_categorical(rng1, pi_logits)
onehot_values = util_fns.onehot(mixture_idcs, nr_mix)
assert onehot_values.shape == (batchsize, height, width, nr_mix)
selection = onehot_values.reshape(xshape[:-1] + (1, nr_mix))
# select logistic parameters
means = jnp.sum(remaining_params[:, :, :, :, :nr_mix] * selection, axis=4)
pre_act_scales = jnp.sum(remaining_params[:, :, :, :, nr_mix:2 * nr_mix] *
selection,
axis=4)
coeffs = jnp.sum(
jax.nn.tanh(remaining_params[:, :, :, :, 2 * nr_mix:3 * nr_mix]) *
selection,
axis=4)
u = jax.random.uniform(rng2, means.shape, minval=1e-5, maxval=1. - 1e-5)
standard_logistic = jnp.log(u) - jnp.log(1. - u)
scale = 1. / jax.nn.softplus(pre_act_scales)
x = means + scale * standard_logistic
x0 = jnp.clip(x[:, :, :, 0], a_min=-1., a_max=1.)
# TODO(emielh) although this is typically how it is implemented, technically
# one should first round x0 to the grid before using it. It does not matter
# too much since it is only used linearly.
x1 = jnp.clip(x[:, :, :, 1] + coeffs[:, :, :, 0] * x0, a_min=-1., a_max=1.)
x2 = jnp.clip(x[:, :, :, 2] + coeffs[:, :, :, 1] * x0 +
coeffs[:, :, :, 2] * x1,
a_min=-1.,
a_max=1.)
sample_x = jnp.concatenate(
[x0[:, :, :, None], x1[:, :, :, None], x2[:, :, :, None]], axis=3)
return sample_x
def log_prob(self, x, dist_params):
"""Computes log prob."""
assert x.dtype == jnp.int32
assert x.shape[:-1] == dist_params.shape[:-1], (
f' for {x.shape} and {dist_params.shape}')
assert dist_params.shape[-1] == self.n_classes * self.n_channels
logits = dist_params.reshape(*x.shape, self.n_classes)
x_onehot = util_fns.onehot(x, num_classes=self.n_classes)
log_probs = jax.nn.log_softmax(logits, axis=-1)
log_probs = jnp.sum(x_onehot * log_probs, axis=-1)
return log_probs
def log_prob_vector_future_given_past(self, logits, x_past, stage):
probs = jax.nn.softmax(logits, axis=-1)
if self.num_input_classes > self.num_output_classes:
# We have to pad probs with empty probabilities for augmented classes.
pad_size = self.num_input_classes - self.num_output_classes
# Only padding at the end of the last axis.
padding = ((0, 0), ) * (len(logits.shape) - 1) + ((0, pad_size), )
# Vector is zero-padded since it is in log-space.
probs = jnp.pad(probs,
pad_width=padding,
mode='constant',
constant_values=0)
stage_reversed = self.num_stages - 1 - stage
transition_future = self.cum_matmul_transition_matrices[stage_reversed]
transition_single_step = self.transition_matrices[stage_reversed]
probs_future = self.transform_with_matrix(probs, transition_future)
x_past_onehot = util_fns.onehot(x_past, self.num_input_classes)
# We only select possible futures:
num_data_axes = len(x_past.shape) - 1 # minus batch size.
new_axes = tuple(range(1, num_data_axes + 1))
possible_futures = jnp.sum(
jnp.expand_dims(transition_single_step, axis=new_axes) *
x_past_onehot[Ellipsis, None],
axis=-2)
# Collect logits given past, using only possible futures.
infty = 1e20
logits_given_past = jnp.log(probs_future * possible_futures +
1e-10) - (1 - possible_futures) * infty
# Forces stability. Corresponds to -jnp.log(prob_past[..., None]) but
# this is numerically more stable.
log_probs = logits_given_past - jax.nn.logsumexp(
logits_given_past, axis=-1, keepdims=True)
return log_probs
def sample_from_discretized_mix_logistic(rng, params, nr_mix):
"""Sample from discretized mix logistic distribution, channel-independent."""
channels = (params.shape[-1] // nr_mix - 1) // 2
xshape = params.shape[:-1] + (channels, )
batchsize = xshape[0]
spatial_dims = xshape[1:-1]
# Unpack parameters.
pi_logits = params[Ellipsis, :nr_mix]
remaining_params = params[Ellipsis, nr_mix:].reshape(*xshape, nr_mix * 2)
means = remaining_params[Ellipsis, :nr_mix]
means = means + jnp.reshape(
jnp.linspace(-1. + 1 / nr_mix, 1 - 1 / nr_mix, nr_mix),
(1, ) * len(xshape) + (nr_mix, ))
log_scales = remaining_params[Ellipsis, nr_mix:2 * nr_mix]
log_scales = log_scales - jnp.log(nr_mix)
# Sample mixture indicator from softmax.
rng1, rng2 = jax.random.split(rng)
mixture_idcs = sample_categorical(rng1, pi_logits)
onehot_values = util_fns.onehot(mixture_idcs, nr_mix)
assert onehot_values.shape == (batchsize, ) + spatial_dims + (nr_mix, )
selection = onehot_values.reshape(xshape[:-1] + (1, nr_mix))
# Select logistic parameters.
means = jnp.sum(means * selection, axis=-1)
log_scales = jnp.sum(log_scales * selection, axis=-1)
log_scales = jnp.clip(log_scales, a_min=-7.)
u = jax.random.uniform(rng2, means.shape, minval=1e-5, maxval=1. - 1e-5)
standard_logistic = jnp.log(u) - jnp.log(1. - u)
sample_x = means + jnp.exp(log_scales) * standard_logistic
sample_x = jnp.clip(sample_x, a_min=-1., a_max=1.)
return sample_x
