  Normalizing flows are a flexible class of probability distributions,
expressed as transformations of a simple base distribution. A limitation of
standard normalizing flows is representing distributions with heavy tails,
which arise in applications to both density estimation and variational
inference. A popular current solution to this problem is to use a heavy tailed
base distribution. Examples include the tail adaptive flow (TAF) methods of
Laszkiewicz et al (2022). We argue this can lead to poor performance due to the
difficulty of optimising neural networks, such as normalizing flows, under
heavy tailed input. This problem is demonstrated in our paper. We propose an
alternative: use a Gaussian base distribution and a final transformation layer
which can produce heavy tails. We call this approach tail transform flow (TTF).
Experimental results show this approach outperforms current methods, especially
when the target distribution has large dimension or tail weight.
