  We present a particle flow realization of Bayes' rule, where an ODE-based
neural operator is used to transport particles from a prior to its posterior
after a new observation. We prove that such an ODE operator exists. Its neural
parameterization can be trained in a meta-learning framework, allowing this
operator to reason about the effect of an individual observation on the
posterior, and thus generalize across different priors, observations and to
sequential Bayesian inference. We demonstrated the generalization ability of
our particle flow Bayes operator in several canonical and high dimensional
examples.
