Cubic-Spline Flows
This work addresses the problem of slow inversion in autoregressive flows for researchers and practitioners in machine learning, offering a faster alternative with competitive density estimation, though it is incremental as it builds on existing coupling transform methods.
The paper tackled the trade-off between speed and accuracy in normalizing flows by introducing cubic-spline flows, which use monotonic cubic splines and LU-decomposed linear layers to achieve high-quality image generation and close the performance gap with autoregressive flows on density-estimation tasks.
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.