Mean-Field Path-Integral Diffusion: From Samples to Interacting Agents

TL;DR

This paper introduces Mean-Field Path-Integral Diffusion (MF-PID), a novel framework where interacting agents coordinate through shared statistics to improve sampling efficiency and control in generative models.

Contribution

MF-PID unifies generative modeling and multi-agent control via a mean-field approach, providing analytically tractable regimes and exact guidance results for distribution matching.

Findings

MF-PID achieves 19-24% reduction in control energy in energy system applications.

Identifies two analytically tractable regimes: LQG and Gaussian-mixture.

Exact linear guidance interpolates between initial and target means for quadratic interactions.

Abstract

Independent sample generation is the prevailing paradigm in modern diffusion-based generative models of AI. We ask a different question: can samples \emph{coordinate} through shared population statistics to transport probability mass more efficiently? We introduce Mean-Field Path-Integral Diffusion (MF-PID), a framework in which samples are promoted to interacting agents whose drift depends self-consistently on the evolving population density. The coupling converts distribution matching into a McKean--Vlasov extension of the stochastic optimal transport problem, unifying generative modeling and multi-agent control under the same Hamilton--Jacobi--Bellman/Kolmogorov--Fokker--Planck duality. We identify two analytically tractable regimes: a Linear--Quadratic--Gaussian (LQG) benchmark in which the infinite-dimensional mean-field system reduces to a finite set of Riccati and linear ODEs, and a Gaussian-mixture regime governed by a piecewise-constant protocol that preserves closed-form solvability. For a quadratic interaction potential with schedule $\beta_t$ and zero base drift we prove that the self-consistent MF guidance is the \emph{exact} linear interpolant between initial and target global means -- a result that holds for arbitrary initial and target densities and any $\beta_t$. Applied to demand-response control of energy systems, where agents aggregated into an ensemble are energy consumers (e.g.\ thermal zones within a building), MF-PID achieves 19--24\% reductions in cumulative control energy over independent-agent baselines while matching the prescribed terminal distribution exactly, and reveals how coordination redistributes actuation effort across heterogeneous sub-populations.