Bridging Stochastic Control and Generative Modeling

Overview

Our research explores the interplay between stochastic control and generative modeling, with the goal of developing new tools for decision-making under uncertainty. We study how ideas from diffusion models, time reversal, and stochastic bridges can be used to design feedback control laws for steering both individual system trajectories and entire probability distributions. At the same time, we use stochastic control and backward stochastic differential equations to better understand and improve the training and fine-tuning of generative models. This perspective creates a two-way connection between control and generation, with applications in robotics, autonomous systems, multi-agent coordination, and scientific machine learning.

Key Ideas

• Use ideas from diffusion models, time reversal, and stochastic bridges to design feedback laws for steering stochastic systems to desired states.
• Develop methods to shape entire probability distributions, with applications to multi-agent systems, robotic swarms, and other settings involving collective uncertainty.
• Use stochastic control and backward stochastic differential equations to improve the training, adaptation, and stability of generative models.

Team

Selected Publications

Selected Presentations