SurVAE Flows: Surjections to Bridge the Gap between VAEs and Flows

TL;DR

SurVAE Flows introduce a modular framework combining VAEs and normalizing flows through surjective transformations, enabling exact likelihood computation and lower bounds, unifying several existing methods.

Contribution

The paper proposes SurVAE Flows, a novel framework that unifies VAEs and normalizing flows using surjective transformations, allowing for tractable likelihood estimation and composable operations.

Findings

SurVAE Flows encompass existing methods like dequantization and augmented flows.

The framework enables exact likelihood computation in certain cases.

Common operations can be integrated as layers within SurVAE Flows.

Abstract

Normalizing flows and variational autoencoders are powerful generative models that can represent complicated density functions. However, they both impose constraints on the models: Normalizing flows use bijective transformations to model densities whereas VAEs learn stochastic transformations that are non-invertible and thus typically do not provide tractable estimates of the marginal likelihood. In this paper, we introduce SurVAE Flows: A modular framework of composable transformations that encompasses VAEs and normalizing flows. SurVAE Flows bridge the gap between normalizing flows and VAEs with surjective transformations, wherein the transformations are deterministic in one direction -- thereby allowing exact likelihood computation, and stochastic in the reverse direction -- hence providing a lower bound on the corresponding likelihood. We show that several recently proposed methods, including dequantization and augmented normalizing flows, can be expressed as SurVAE Flows. Finally, we introduce common operations such as the max value, the absolute value, sorting and stochastic permutation as composable layers in SurVAE Flows.