Neural Bayesian Filtering

Sequential estimation under partial observability requires tracking belief distributions that may be high-dimensional, multimodal, and non-Gaussian. Classical Bayesian filters generalize zero-shot to any system whose dynamics can be evaluated, but their representations scale poorly: parametric filters struggle to capture multimodality, and particle filters require exponentially many particles in the state dimension. Generative Distribution Embeddings (GDEs) learn compact representations of complex distributions but provide no mechanism for sequential updates. We present Neural Bayesian Filtering (NBF), a method that combines classical Bayesian filtering with learned distribution embeddings. NBF represents beliefs as embeddings and updates them by sampling particles from a learned conditional generator, propagating them through the system dynamics, and finally re-embedding the resulting particles. For in-family distributions that the embeddings are trained to represent, NBF inherits the zero-shot adaptability of classical filters, but with the benefit that regenerating particles from the embedding at each step also mitigates particle impoverishment. We validate NBF on a pursuit--evasion domain, demonstrating accurate tracking of complex multimodal posteriors, graceful scaling with state dimension, and zero-shot generalization to dynamics held out from training.