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

2026-01-13

AI Summary

Efficient sampling from unnormalized Boltzmann densities remains challenging, particularly in high-dimensional multimodal distributions and Bayesian inference. This work proposes a probability flow ordinary differential equation (ODE) method based on linear stochastic interpolation, which, for the first time, employs a Langevin sampler to jointly draw samples from interpolated distributions and estimate the corresponding velocity field. This approach provides a theoretically grounded initialization and dynamic modeling for the flow ODE, ensuring stability and convergence. By integrating stochastic interpolation, probability flow ODEs, and Langevin diffusion, the method demonstrates efficient and robust sampling performance across a range of high-dimensional multimodal distributions and Bayesian inference tasks.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Probabilistic Programming
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Large language models for search

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 flow ODE. For both applications of the Langevin diffusions, we establish convergence guarantees. 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.

Problem

• sampling
• Boltzmann distribution
• probability flow
• stochastic interpolants
• Langevin dynamics

Innovation

• Stochastic Interpolants
• Langevin Sampling
• Flow ODEs
• Velocity Estimation
• Boltzmann Sampling