From discrete-time policies to continuous-time diffusion samplers: Asymptotic equivalences and faster training

TL;DR

This paper introduces a new approach to training neural diffusion models for sampling from Boltzmann distributions, leveraging asymptotic equivalences and optimized discretization to improve efficiency and performance.

Contribution

It establishes theoretical links between entropic RL and continuous-time diffusion models, and demonstrates how coarse discretization enhances training efficiency and reduces computational costs.

Findings

Theoretical equivalences between objectives in infinitesimal discretization limit.

Coarse discretization improves sample efficiency during training.

Achieves competitive sampling performance with lower computational cost.

Abstract

We study the problem of training neural stochastic differential equations, or diffusion models, to sample from a Boltzmann distribution without access to target samples. Existing methods for training such models enforce time-reversal of the generative and noising processes, using either differentiable simulation or off-policy reinforcement learning (RL). We prove equivalences between families of objectives in the limit of infinitesimal discretization steps, linking entropic RL methods (GFlowNets) with continuous-time objects (partial differential equations and path space measures). We further show that an appropriate choice of coarse time discretization during training allows greatly improved sample efficiency and the use of time-local objectives, achieving competitive performance on standard sampling benchmarks with reduced computational cost.