  Normalizing Flows (NFs) are able to model complicated distributions p(y) with
strong inter-dimensional correlations and high multimodality by transforming a
simple base density p(z) through an invertible neural network under the change
of variables formula. Such behavior is desirable in multivariate structured
prediction tasks, where handcrafted per-pixel loss-based methods inadequately
capture strong correlations between output dimensions. We present a study of
conditional normalizing flows (CNFs), a class of NFs where the base density to
output space mapping is conditioned on an input x, to model conditional
densities p(y|x). CNFs are efficient in sampling and inference, they can be
trained with a likelihood-based objective, and CNFs, being generative flows, do
not suffer from mode collapse or training instabilities. We provide an
effective method to train continuous CNFs for binary problems and in
particular, we apply these CNFs to super-resolution and vessel segmentation
tasks demonstrating competitive performance on standard benchmark datasets in
terms of likelihood and conventional metrics.
