[2604.00283] Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees

Electrical Engineering and Systems Science > Systems and Control arXiv:2604.00283 (eess) [Submitted on 31 Mar 2026] Title:Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees Authors:Yanliang Huang, Peng Xie, Wenyuan Wu, Zhuoqi Zeng, Amr Alanwar View a PDF of the paper titled Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees, by Yanliang Huang and 4 other authors View PDF HTML (experimental) Abstract:We present a data-driven framework for reachability analysis of nonlinear dynamical systems that requires no explicit model. A denoising diffusion probabilistic model learns the time-evolving state distribution of a dynamical system from trajectory data alone. The predicted reachable set takes the form of a sublevel set of a nonconformity score derived from the reconstruction error, with the threshold calibrated via the Learn Then Test procedure so that the probability of excluding a reachable state is bounded with high probability. Experiments on three nonlinear systems, a forced Duffing oscillator, a planar quadrotor, and a high-dimensional reaction-diffusion system, confirm that the empirical miss rate remains below the Probably Approximately Correct (PAC) bound while scaling to state dimensions beyond the reach of classical grid-based and polynomial methods. Comments: Subjects: Systems and Control (eess.SY); Machine Learning (cs.LG) Cite as: arXiv:2604.00283 [eess.SY]   (or arXiv:2604.00283v1 [eess.SY] for this version)   http...