Sequential Monte Carlo (SMC) and Variational Inference (VI) are two families of approximate inference algorithms for Bayesian latent variable models. A body of recent work has focused on constructing a variational family of filtered distributions using SMC. Inspired by this work, we introduce Particle Smoothing Variational Objectives (SVO), a novel backward simulation technique and variational objective constructed from a smoothed approximate posterior. Our method sub-samples auxiliary random variables to enhance the support of the proposal distribution and increase particle diversity. We demonstrate our approach on three benchmark latent nonlinear dynamical systems tasks. SVO consistently outperforms filtered objectives when given fewer Monte Carlo samples.