Cubic-Spline Flows

TL;DR

Cubic-Spline Flows introduce a new invertible coupling transform based on monotonic cubic splines, achieving fast density estimation and sample generation while closing the performance gap with autoregressive flows.

Contribution

The paper presents a novel cubic-spline coupling transform for normalizing flows that improves density estimation performance without sacrificing invertibility or speed.

Findings

Achieves high-quality image generation.

Closes the performance gap with autoregressive flows.

Maintains exact one-pass inverse for efficient computation.

Abstract

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.