  Despite their popularity, to date, the application of normalizing flows on
categorical data stays limited. The current practice of using dequantization to
map discrete data to a continuous space is inapplicable as categorical data has
no intrinsic order. Instead, categorical data have complex and latent relations
that must be inferred, like the synonymy between words. In this paper, we
investigate \emph{Categorical Normalizing Flows}, that is normalizing flows for
categorical data. By casting the encoding of categorical data in continuous
space as a variational inference problem, we jointly optimize the continuous
representation and the model likelihood. Using a factorized decoder, we
introduce an inductive bias to model any interactions in the normalizing flow.
As a consequence, we do not only simplify the optimization compared to having a
joint decoder, but also make it possible to scale up to a large number of
categories that is currently impossible with discrete normalizing flows. Based
on Categorical Normalizing Flows, we propose GraphCNF a permutation-invariant
generative model on graphs. GraphCNF implements a three step approach modeling
the nodes, edges and adjacency matrix stepwise to increase efficiency. On
molecule generation, GraphCNF outperforms both one-shot and autoregressive
flow-based state-of-the-art.
