Cubic-Spline Flows

Conor Durkan, Artur Bekasovs, Iain Murray, Georgios Papamakarios

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 onepass inverse, can be used to generate high-quality images, and closes the gap with autoregressive flows on a suite of density-estimation tasks.
Original languageEnglish
Title of host publicationFirst workshop on Invertible Neural Networks and Normalizing Flows
Subtitle of host publicationat ICML 2019
Number of pages7
Publication statusE-pub ahead of print - 15 Jun 2019
EventWorkshop on Invertible Neural Nets and Normalizing Flows: ICML 2019 - Long Beach, United States
Duration: 15 Jun 201915 Jun 2019
Conference number: 1


WorkshopWorkshop on Invertible Neural Nets and Normalizing Flows
Abbreviated titleINNF
CountryUnited States
CityLong Beach
Internet address


Dive into the research topics of 'Cubic-Spline Flows'. Together they form a unique fingerprint.

Cite this