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