  Normalizing flows have emerged as an important family of deep neural networks
for modelling complex probability distributions. In this note, we revisit their
coupling and autoregressive transformation layers as probabilistic graphical
models and show that they reduce to Bayesian networks with a pre-defined
topology and a learnable density at each node. From this new perspective, we
provide three results. First, we show that stacking multiple transformations in
a normalizing flow relaxes independence assumptions and entangles the model
distribution. Second, we show that a fundamental leap of capacity emerges when
the depth of affine flows exceeds 3 transformation layers. Third, we prove the
non-universality of the affine normalizing flow, regardless of its depth.
