Diffusion as Prior Construction: A Bayesian View of Communication in Multi-Agent POMDPs

In partially observable multi-agent systems, naive belief exchange often leads to epistemic overconfidence and data incest due to unknown correlations in reused information. To address this, we reinterpret inter-agent communication as dynamic prior construction, where a diffusion step systematically precedes observation-based Bayesian correction. Theoretically, we demonstrate that this diffusion operator acts as a tractable, convex approximation of product-form priors, guaranteeing variance reduction and mitigating false certainty. An optional post-diffusion step further enhances robustness under non-stationary latent dynamics. Empirically, across both static and dynamic environments, the proposed framework significantly improves inter-agent belief consensus without sacrificing latent state accuracy, while remaining fully compatible with gradient-based representation learning.