Sampling via Stochastic Interpolants by Langevin-based Velocity and Initialization Estimation in Flow ODEs

TL;DR

This paper introduces a new sampling method using Langevin-based velocity and initialization estimation within flow ODEs, improving efficiency and robustness for complex distributions and Bayesian inference.

Contribution

It presents a novel approach combining Langevin samplers with probability flow ODEs, providing convergence guarantees and enhanced sampling performance.

Findings

Efficient sampling from challenging multimodal distributions.

Theoretical convergence guarantees for the proposed method.

Effective in high-dimensional Bayesian inference tasks.

Abstract

We propose a novel method for sampling from unnormalized Boltzmann densities based on a probability flow ordinary differential equation (ODE) derived from linear stochastic interpolants. The key innovation of our approach is the use of a sequence of Langevin samplers to enable efficient simulation of the flow. Specifically, these Langevin samplers are employed (i) to generate samples from the interpolant distribution at intermediate times and (ii) to construct, starting from these intermediate times, a robust estimator of the velocity field governing the probability flow ODE. Theoretically, we provide convergence guarantees for both Langevin components, and establish a non-asymptotic convergence rate for the probability flow ODE. Extensive numerical experiments demonstrate the efficiency of the proposed method on challenging multimodal distributions across a range of dimensions, as well as its effectiveness in Bayesian inference tasks.