  Normalizing flows model complex probability distributions by combining a base
distribution with a series of bijective neural networks. State-of-the-art
architectures rely on coupling and autoregressive transformations to lift up
invertible functions from scalars to vectors. In this work, we revisit these
transformations as probabilistic graphical models, showing they reduce to
Bayesian networks with a pre-defined topology and a learnable density at each
node. From this new perspective, we propose the graphical normalizing flow, a
new invertible transformation with either a prescribed or a learnable graphical
structure. This model provides a promising way to inject domain knowledge into
normalizing flows while preserving both the interpretability of Bayesian
networks and the representation capacity of normalizing flows. We show that
graphical conditioners discover relevant graph structure when we cannot
hypothesize it. In addition, we analyze the effect of $\ell_1$-penalization on
the recovered structure and on the quality of the resulting density estimation.
Finally, we show that graphical conditioners lead to competitive white box
density estimators. Our implementation is available at
https://github.com/AWehenkel/DAG-NF.
