Abstract: Decision making under uncertainty is critical to real-world, autonomous systems. Model Predictive Control (MPC) methods have demonstrated favorable performance in practice, but remain limited when dealing with complex probability distributions. In this paper, we propose a generalization of MPC that represents a multitude of solutions as posterior distributions. By casting MPC as a Bayesian inference problem, we employ variational methods for posterior computation, naturally encoding the complexity and multi-modality of the decision making problem. We propose a Stein variational gradient descent method to estimate the posterior over control parameters, given a cost function and a sequence of state observations. We show that this framework leads to successful planning in challenging, non-convex optimal control problems.