A theory of continuous generative flow networks

TL;DR

This paper extends generative flow networks (GFlowNets) to continuous and hybrid spaces, providing a unified theory and demonstrating their effectiveness in probabilistic inference tasks.

Contribution

It introduces a generalized theory for GFlowNets covering discrete, continuous, and hybrid spaces, and empirically validates their advantages over traditional methods.

Findings

Generalized GFlowNets perform well on continuous and hybrid spaces.

Theoretical insights highlight key assumptions for GFlowNet success.

Empirical results show strong performance compared to non-GFlowNet baselines.

Abstract

Generative flow networks (GFlowNets) are amortized variational inference algorithms that are trained to sample from unnormalized target distributions over compositional objects. A key limitation of GFlowNets until this time has been that they are restricted to discrete spaces. We present a theory for generalized GFlowNets, which encompasses both existing discrete GFlowNets and ones with continuous or hybrid state spaces, and perform experiments with two goals in mind. First, we illustrate critical points of the theory and the importance of various assumptions. Second, we empirically demonstrate how observations about discrete GFlowNets transfer to the continuous case and show strong results compared to non-GFlowNet baselines on several previously studied tasks. This work greatly widens the perspectives for the application of GFlowNets in probabilistic inference and various modeling settings.