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

arXiv (Cornell University)

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.

Authors 6

1. Chenguang Duan Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik , RWTH Aachen University , Templergraben 55 , 52056 Aachen , Germany

2. Yuling Jiao

   Wuhan University · Wuhan Business University

   Affiliation as printed

   School of Artificial Intelligence , Wuhan University , Wuhan , Hubei 430072 , China

3. Gabriele Steidl

   Technische Universität Berlin

   Affiliation as printed

   Institut für Mathematik , Technische Universität Berlin , Straße des 17. Juni 136 , 10623 Berlin , Germany

4. Christian Wald

   Technische Universität Berlin

   Affiliation as printed

   Institut für Mathematik , Technische Universität Berlin , Straße des 17. Juni 136 , 10623 Berlin , Germany

5. Jerry Zhijian Yang

   Wuhan University

   Affiliation as printed

   School of Mathematics and Statistics , Wuhan University , Wuhan , Hubei 430072 , China

6. Ruizhe Zhang

   Wuhan University

   Affiliation as printed

   School of Mathematics and Statistics , Wuhan University , Wuhan , Hubei 430072 , China