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

Independent sample generation is the prevailing paradigm in modern diffusion-based generative models of AI. We ask a different question: can samples 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. 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 βt and zero base drift we prove that the self-consistent MF guidance is the exact linear interpolant between initial and target global means -- a result that holds for arbitrary initial and target densities and any βt. Applied to demand-response control of energy systems, where agents aggregated into an ensemble are energy consumers (e.g. The energy saving is independent of the number of zones per building (d = 1-32 tested), confirming that the linear guidance formula broadcasts a single d-vector with O(d) communication and grows mildly in compute (sub-cubically for d 32, asymptotically O(d3) for d 1). Introduction Generative AI has been transformed by diffusion models, which frame sample generation as a stochastic process steered from noise to data [1-3]. A key structural feature of these models -- shared with other generative models, e.g. Similarly, stochastic optimal transport (SOT) and Schrödinger bridge formulations [6-8] cast distribution matching as an independent-particle path optimization, yielding tractable convolutions of Green functions but discarding inter-particle information; stochastic interpolants [9] construct flexible transport bridges between arbitrary densities via tunable continuous-time stochastic processes, recovering the Schrödinger bridge as a special limit -- again in an independent-particle framework.