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

2025-11-19

AI Summary

This work addresses the closed-loop stability problem arising when diffusion policies are coupled with physical dynamical systems (e.g., robots). Methodologically, it introduces a novel theoretical framework by parallelly coupling the denoising process with plant dynamics, thereby constructing a closed-loop control system under inverse-time diffusion modeling; leveraging Lyapunov stability theory, it derives an analytically tractable stability criterion—explicitly linking controller stability to the variance characteristics of demonstration data, thus establishing the first quantitative mapping from data statistics to control stability. Contributions include: (1) defining the theoretical stability boundary for diffusion-driven control; (2) enabling high-real-time decision-making via significantly reduced inference latency; and (3) providing a verifiable control framework for fast, stable imitation learning grounded in demonstration data.

Technology Category

• Intelligent Robots: Behavior Learning & Control
• Computer Vision: Diffusion Models for Vision
• Machine Learning: Imitation Learning & Inverse Reinforcement Learning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

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.

Problem

• Studying theoretical stability bounds for coupled plant-denoising dynamics
• Addressing real-time limitations of diffusion policies' computational demands
• Developing framework for faster imitation learning with stability guarantees

Innovation

• Partial denoising during action execution
• Coupled plant and denoising dynamics analysis
• Stability bounds framework for diffusion policies