Mean-field path-integral diffusion from samples to interacting agents

Abstract

Abstract Moving probability distributions in the context of stochastic processes efficiently is central to modern generative modeling, uncertainty quantification, and control of large engineered systems. Most current methods generate temporal trajectories independently, leaving open whether the trajectories can cooperate through shared population information to reduce transport cost. Here we show that mean-field path-integral diffusion turns this question into a self-consistent stochastic control problem in which each trajectory responds to the evolving population. In a broad linear-quadratic setting, the problem reduces to a finite system of ordinary differential equations. For quadratic interactions with no background drift, we prove that the optimal population guidance is exactly the straight-line interpolation between the initial and target means, for arbitrary endpoint distributions with finite means. This yields an explicit construction for mixture targets. In demand-response control of multi-zone buildings, the method reduces control energy by 19–24% while maintaining the desired final distribution. These results suggest a practical route to coordinated generative transport for energy and other large-agent systems.