Liouville Flow Importance Sampler

TL;DR

The Liouville Flow Importance Sampler (LFIS) introduces a flow-based neural model that transports samples along a learned velocity field to efficiently estimate complex unnormalized distributions, achieving state-of-the-art results.

Contribution

LFIS is the first to combine flow-based models with a PDE-guided training method for importance sampling of unnormalized densities.

Findings

LFIS achieves state-of-the-art performance on benchmark problems.

LFIS provides unbiased, consistent statistical estimates.

LFIS effectively transports samples along learned velocity fields.

Abstract

We present the Liouville Flow Importance Sampler (LFIS), an innovative flow-based model for generating samples from unnormalized density functions. LFIS learns a time-dependent velocity field that deterministically transports samples from a simple initial distribution to a complex target distribution, guided by a prescribed path of annealed distributions. The training of LFIS utilizes a unique method that enforces the structure of a derived partial differential equation to neural networks modeling velocity fields. By considering the neural velocity field as an importance sampler, sample weights can be computed through accumulating errors along the sample trajectories driven by neural velocity fields, ensuring unbiased and consistent estimation of statistical quantities. We demonstrate the effectiveness of LFIS through its application to a range of benchmark problems, on many of which LFIS achieved state-of-the-art performance.