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

arXiv:2605.00007v1 Announce Type: cross
Abstract: Independent sample generation is the prevailing paradigm in modern diffusion-based generative models of AI. We ask a different question: can samples emphcoordinate 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 emphexact 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.