  Normalising flows are tractable probabilistic models that leverage the power
of deep learning to describe a wide parametric family of distributions, all
while remaining trainable using maximum likelihood. We discuss how these
methods can be further improved based on insights from robust (in particular,
resistant) statistics. Specifically, we propose to endow flow-based models with
fat-tailed latent distributions such as multivariate Student's $t$, as a simple
drop-in replacement for the Gaussian distribution used by conventional
normalising flows. While robustness brings many advantages, this paper explores
two of them: 1) We describe how using fatter-tailed base distributions can give
benefits similar to gradient clipping, but without compromising the asymptotic
consistency of the method. 2) We also discuss how robust ideas lead to models
with reduced generalisation gap and improved held-out data likelihood.
Experiments on several different datasets confirm the efficacy of the proposed
approach in both regards.
