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

Anand Jerry George, Nicolas Macris
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:2980-2988, 2025.

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 this Paper

BibTeX
@InProceedings{pmlr-v258-george25a, 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}, pages = {2980--2988}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/george25a/george25a.pdf}, url = {https://proceedings.mlr.press/v258/george25a.html}, 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.} }
Endnote
%0 Conference Paper %T Sampling in High-Dimensions using Stochastic Interpolants and Forward-Backward Stochastic Differential Equations %A Anand Jerry George %A Nicolas Macris %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-george25a %I PMLR %P 2980--2988 %U https://proceedings.mlr.press/v258/george25a.html %V 258 %X 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.
APA
George, A.J. & Macris, N.. (2025). Sampling in High-Dimensions using Stochastic Interpolants and Forward-Backward Stochastic Differential Equations. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:2980-2988 Available from https://proceedings.mlr.press/v258/george25a.html.

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