Mean-Field Path-Integral Diffusion: From Samples to Interacting Agents
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918476862455808 |
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| author | Chertkov, Michael |
| author_facet | Chertkov, Michael |
| contents | 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 $β_t$ 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 $β_t$. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_00007 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mean-Field Path-Integral Diffusion: From Samples to Interacting Agents Chertkov, Michael Optimization and Control Artificial Intelligence Machine Learning 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 $β_t$ 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 $β_t$. 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. |
| title | Mean-Field Path-Integral Diffusion: From Samples to Interacting Agents |
| topic | Optimization and Control Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2605.00007 |