  Particle Filtering (PF) methods are an established class of procedures for
performing inference in non-linear state-space models. Resampling is a key
ingredient of PF, necessary to obtain low variance likelihood and states
estimates. However, traditional resampling methods result in PF-based loss
functions being non-differentiable with respect to model and PF parameters. In
a variational inference context, resampling also yields high variance gradient
estimates of the PF-based evidence lower bound. By leveraging optimal transport
ideas, we introduce a principled differentiable particle filter and provide
convergence results. We demonstrate this novel method on a variety of
applications.
