You say Normalizing Flows I see Bayesian Networks
This provides theoretical insights into normalizing flows for researchers in probabilistic machine learning, but it is incremental as it builds on existing frameworks.
The paper revisits normalizing flows as Bayesian networks, showing that stacking transformations relaxes independence assumptions and entangles distributions, and proves that affine normalizing flows are non-universal regardless of depth.
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.