# Sampling in High-Dimensions using Stochastic Interpolants and Forward-Backward Stochastic Differential Equations

arXiv: https://arxiv.org/abs/2502.00355 · HTML: https://mlsanity.com/paper/2502.00355/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 1 Feb 2025.

## Abstract (arXiv)

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.