You say Normalizing Flows I see Bayesian Networks

Understand

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.