Neural Bayesian Filtering

Sequential estimation under partial observability requires tracking beliefs 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 have no sequential update. We present Neural Bayesian Filtering (NBF), which represents beliefs as embeddings and approximates their Bayesian update. At each step, NBF samples particles from a learned conditional generator, propagates them through the dynamics, and embeds the propagated set, weighted by the likelihood of the new observation. Regenerating the set from the embedding at each step, rather than resampling a surviving pool, mitigates the risk of impoverishment that degrades particle filters. The system dynamics and likelihood enter only through propagation and weighting, so NBF retains zero-shot adaptability to new dynamics as long as the beliefs they produce fall within the family the embedding was trained on. Training the GDE to represent that family requires only the states realized at training time. We validate NBF on Lorenz-96 and a pursuit--evasion domain, showing graceful scaling with state dimension, accurate tracking of multimodal posteriors, and zero-shot generalization to dynamics and likelihoods held out from training.