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

• URL: http://arxiv.org/abs/2605.00007v1
• Date: Mon, 23 Feb 2026 21:14:06 GMT
• Title: Mean-Field Path-Integral Diffusion: From Samples to Interacting Agents
• Abstract summary: Mean-Field Path-Integral Diffusion (MF-PID) is a framework in which samples are promoted to interacting agents whose drift depends self-consistently on the evolving population density.<n>MF-PID achieves 19--24% reductions in cumulative control energy over independent-agent baselines while matching the prescribed terminal distribution exactly.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $β_t$ 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.

Related papers

• Generative Nested Sampling of Atomistic Thermodynamic Landscapes [37.547720439639015]
  Flow-based nested sampling has removed the bottleneck for gravitational-wave (GW) inference.<n>We show that LJ disks in PBC reduce energy evaluations by over two orders of magnitude and wall-clock time by roughly one third.<n>For LJ disks in PBC, the algorithm reduces energy evaluations by over two orders of magnitude and wall-clock time by roughly one third.
  arXiv  Detail & Related papers  (2026-09-02T22:21:10Z)
• Constrained Diffusion Models with Primal-Dual Inference [76.64466170898369]
  We develop constrained diffusion models with primal-dual inference (PDI)<n>PDI infers the optimal primal distribution and its parametrizing dual variable.<n>We evaluate PDI on constrained sampling from a mixture of Gaussians, wireless resource allocation, and portfolio management.
  arXiv  Detail & Related papers  (2026-06-15T18:32:33Z)
• Entropy-Controlled Flow Matching [0.08460698440162889]
  We propose a constrained variational principle over continuity-equation paths enforcing a global entropy-rate budget d/dt H(mu_t) >= -lambda.<n>We obtain certificate-style mode-coverage and density-floor guarantees with Lipschitz, and construct near-optimal counterexamples for unconstrained flow matching.
  arXiv  Detail & Related papers  (2026-02-25T06:07:01Z)
• Stability and Generalization of Push-Sum Based Decentralized Optimization over Directed Graphs [55.77845440440496]
  Push-based decentralized communication enables optimization over communication networks, where information exchange may be asymmetric.<n>We develop a unified uniform-stability framework for the Gradient Push (SGP) algorithm.<n>A key technical ingredient is an imbalance-aware generalization bound through two quantities.
  arXiv  Detail & Related papers  (2026-02-24T05:32:03Z)
• Energy-Based Coarse-Graining in Molecular Dynamics: A Flow-Based Framework without Data [0.0]
  Coarse-grained (CG) models provide an effective route to reducing the complexity of molecular simulations.<n>We introduce a fully data-free, generative framework for CG that directly targets the all-atom Boltzmann distribution.<n>We show that the method captures all relevant modes of the Boltzmann distribution, reconstructs atomic configurations, and automatically learns physically meaningful CG representations.
  arXiv  Detail & Related papers  (2025-04-29T17:05:27Z)
• Steering Large Agent Populations using Mean-Field Schrodinger Bridges with Gaussian Mixture Models [13.03355083378673]
  Mean-Field Schrodinger Bridge (MFSB) problem is an optimization problem aiming to find the minimum effort control policy.<n>In the context of multi-agent control, the objective is to control the configuration of a swarm of identical, interacting cooperative agents.
  arXiv  Detail & Related papers  (2025-03-31T04:01:04Z)
• Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplers [49.97755400231656]
  We present the first performance guarantee with explicit dimensional dependencies for general score-mismatched diffusion samplers.<n>We show that score mismatches result in an distributional bias between the target and sampling distributions, proportional to the accumulated mismatch between the target and training distributions.<n>This result can be directly applied to zero-shot conditional samplers for any conditional model, irrespective of measurement noise.
  arXiv  Detail & Related papers  (2024-10-17T16:42:12Z)
• Bellman Diffusion: Generative Modeling as Learning a Linear Operator in the Distribution Space [72.52365911990935]
  We introduce Bellman Diffusion, a novel DGM framework that maintains linearity in MDPs through gradient and scalar field modeling. Our results show that Bellman Diffusion achieves accurate field estimations and is a capable image generator, converging 1.5x faster than the traditional histogram-based baseline in distributional RL tasks.
  arXiv  Detail & Related papers  (2024-10-02T17:53:23Z)
• Stochastic Semi-Gradient Descent for Learning Mean Field Games with Population-Aware Function Approximation [16.00164239349632]
  Mean field games (MFGs) model interactions in large-population multi-agent systems through population distributions.<n>Traditional learning methods for MFGs are based on fixed-point iteration (FPI), where policy updates and induced population distributions are computed separately and sequentially.<n>We propose a novel perspective that treats the policy and population as a unified parameter controlling the game dynamics.
  arXiv  Detail & Related papers  (2024-08-15T14:51:50Z)
• Delta-AI: Local objectives for amortized inference in sparse graphical models [64.5938437823851]
  We present a new algorithm for amortized inference in sparse probabilistic graphical models (PGMs) Our approach is based on the observation that when the sampling of variables in a PGM is seen as a sequence of actions taken by an agent, sparsity of the PGM enables local credit assignment in the agent's policy learning objective. We illustrate $Delta$-AI's effectiveness for sampling from synthetic PGMs and training latent variable models with sparse factor structure.
  arXiv  Detail & Related papers  (2023-10-03T20:37:03Z)
• Adaptive Annealed Importance Sampling with Constant Rate Progress [68.8204255655161]
  Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution. We propose the Constant Rate AIS algorithm and its efficient implementation for $alpha$-divergences.
  arXiv  Detail & Related papers  (2023-06-27T08:15:28Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.