Unifying Model Predictive Path Integral Control, Reinforcement Learning, and Diffusion Models for Optimal Control and Planning

Model Predictive Path Integral (MPPI) control, Reinforcement Learning (RL), and Diffusion Models have each demonstrated strong performance in trajectory optimization, decision-making, and motion planning. However, these approaches have traditionally been treated as distinct methodologies with separate optimization frameworks. In this work, we establish a unified perspective that connects MPPI, RL, and Diffusion Models through gradient-based optimization on the Gibbs measure. We first show that MPPI can be interpreted as performing gradient ascent on a smoothed energy function. We then demonstrate that Policy Gradient methods reduce to MPPI when treating policy parameters as control variables under a fixed initial state. Additionally, we establish that the reverse sampling process in diffusion models follows the same update rule as MPPI.