Theoretical Closed-loop Stability Bounds for Dynamical System Coupled with Diffusion Policies

Diffusion Policy has shown great performance in robotic manipulation tasks under stochastic perturbations, due to its ability to model multimodal action distributions. Nonetheless, its reliance on a computationally expensive reverse-time diffusion (denoising) process, for action inference, makes it challenging to use for real-time applications where quick decision-making is mandatory. This work studies the possibility of conducting the denoising process only partially before executing an action, allowing the plant to evolve according to its dynamics in parallel to the reverse-time diffusion dynamics ongoing on the computer. In a classical diffusion policy setting, the plant dynamics are usually slow and the two dynamical processes are uncoupled. Here, we investigate theoretical bounds on the stability of closed-loop systems using diffusion policies when the plant dynamics and the denoising dynamics are coupled. The contribution of this work gives a framework for faster imitation learning and a metric that yields if a controller will be stable based on the variance of the demonstrations.