mlsanityData to 7 Oct 2026

Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees

arXiv 2604.00283 ↗First posted 31 Mar 2026eess.SY cs.LG cs.SYcited by 0

On the map: Diffusion models → Diffusion and flow policies for robotics

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models. Builds on 20 of its 30 references that are in the map. First posted on arXiv 31 Mar 2026.

Builds on

20 of 30 references.

References · 20

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  3. 2017FiLM: Visual Reasoning with a General Conditioning Layercited by 2,286
  4. 2015Variational Inference with Normalizing Flowscited by 2,161
  5. 2019Neural Spline Flowscited by 590
  6. 2023Your Diffusion Model is Secretly a Zero-Shot Classifiercited by 301
  7. 2016Least Ambiguous Set-Valued Classifiers with Bounded Error Levelscited by 270
  8. 2021Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Controlcited by 256
  9. 2021Testing for Outliers with Conformal p-valuescited by 133
  10. 2022Denoising diffusion models for out-of-distribution detectioncited by 102
  11. 2020DeepReach: A Deep Learning Approach to High-Dimensional Reachabilitycited by 81
  12. 2019Data-Driven Reachable Set Computation using Adaptive Gaussian Process Classification and Monte Carlo Methodscited by 14
8 more
  1. 2021Data-Driven Reachability Analysis from Noisy Datacited by 14
  2. 2021Data-Driven Reachability Analysis with Christoffel Functionscited by 12
  3. 2023Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inferencecited by 9
  4. 2023Data-driven Reachability using Christoffel Functions and Conformal Predictioncited by 6
  5. 2024Statistical Reachability Analysis of Stochastic Cyber-Physical Systems under Distribution Shiftcited by 4
  6. 2025Data-Driven Nonconvex Reachability Analysis using Exact Multiplicationcited by 2
  7. 2026Scalable Data-Driven Reachability Analysis and Control via Koopman Operators with Conformal Coverage Guaranteescited by 1
  8. 2026Conformalized Data-Driven Reachability Analysis with PAC Guaranteescited by 1

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  1. 2024Denoising Diffusion-Based Control of Nonlinear Systems
  2. 2026PIDM-DP: Physics-Informed Diffusion with Dormand-Prince Integration for Chaotic System Identification and State Reconstruction across Multiple Dynamical Regimes
  3. 2025DDAT: Diffusion Policies Enforcing Dynamically Admissible Robot Trajectories
  4. 2023Trajectory Generation, Control, and Safety with Denoising Diffusion Probabilistic Models
  5. 2025Dynamics-aware Diffusion Models for Planning and Control
  6. 2026Grounding Generative Policies in Physics: Optimization-Guided Diffusion for Robot Control
  7. 2025Controllable Motion Generation via Diffusion Modal Coupling
  8. 2024DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimization