Score Matching Diffusion Based Feedback Control and Planning of Nonlinear Systems

ArXi:2504.09836v2 Announce Type: replace-cross In this paper, we propose a deterministic diffusion-based framework for controlling the probability density of nonlinear control-affine systems, with theoretical guarantees for drift-free and linear time-invariant (LTI) dynamics. The central idea is to first excite the system with white noise so that a forward diffusion process explores the reachable regions of state space, and then to design a deterministic feedback law that acts as a denoising mechanism driving the system back toward a desired target distribution ed on the target set.