  A normalizing flow models a complex probability density as an invertible
transformation of a simple density. The invertibility means that we can
evaluate densities and generate samples from a flow. In practice,
autoregressive flow-based models are slow to invert, making either density
estimation or sample generation slow. Flows based on coupling transforms are
fast for both tasks, but have previously performed less well at density
estimation than autoregressive flows. We stack a new coupling transform, based
on monotonic cubic splines, with LU-decomposed linear layers. The resulting
cubic-spline flow retains an exact one-pass inverse, can be used to generate
high-quality images, and closes the gap with autoregressive flows on a suite of
density-estimation tasks.
