On Diffusion Models for Multi-Agent Partial Observability: Shared Attractors, Error Bounds, and Composite Flow

Multiagent systems grapple with partial observability (PO), and the decentralized POMDP (Dec-POMDP) model highlights the fundamental nature of this challenge. Whereas recent approaches to addressing PO have appealed to deep learning models, providing a rigorous understanding of how these models and their approximation errors aect agents' handling of PO and their interactions remain a challenge. In addressing this challenge, we investigate reconstructing global states from local action-observation histories in Dec-POMDPs using diusion models. We rst nd that diusion models conditioned on local history represent possible states as stable xed points. In collectively observable (CO) Dec-POMDPs, individual diusion models conditioned on agents' local histories share a unique xed point corresponding to the global state, while in non-CO settings, shared xed points yield a distribution of possible states given joint history. We further nd that, with deep learning approximation errors, xed points can deviate from true states and the deviation is negatively correlated to the Jacobian rank. Inspired by this low-rank property, we bound a deviation by constructing a surrogate linear regression model that approximates the local behavior of a diusion model. With this bound, we propose a composite diusion process iterating over agents with theoretical convergence guarantees to the true state.