Sampling in High-Dimensions Using Stochastic Interpolants and Forward-Backward Stochastic Differential Equations
Abstract
We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified target distribution in finite time. Our approach relies on the stochastic interpolants framework to define a time-indexed collection of probability densities that bridge a Gaussian distribution to the target distribution. Subsequently, we derive a diffusion process that obeys the aforementioned probability density at each time instant. Obtaining such a diffusion process involves solving certain Hamilton-Jacobi-Bellman PDEs. We solve these PDEs using the theory of forward-backward stochastic differential equations (FBSDE) together with machine learning-based methods. Through numerical experiments, we demonstrate that our algorithm can effectively draw samples from distributions that conventional methods struggle to handle.
Cite
Text
George and Macris. "Sampling in High-Dimensions Using Stochastic Interpolants and Forward-Backward Stochastic Differential Equations." Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, 2025.Markdown
[George and Macris. "Sampling in High-Dimensions Using Stochastic Interpolants and Forward-Backward Stochastic Differential Equations." Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, 2025.](https://mlanthology.org/aistats/2025/george2025aistats-sampling/)BibTeX
@inproceedings{george2025aistats-sampling,
title = {{Sampling in High-Dimensions Using Stochastic Interpolants and Forward-Backward Stochastic Differential Equations}},
author = {George, Anand Jerry and Macris, Nicolas},
booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics},
year = {2025},
pages = {2980-2988},
volume = {258},
url = {https://mlanthology.org/aistats/2025/george2025aistats-sampling/}
}