# Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees

arXiv: https://arxiv.org/abs/2604.00283 · HTML: https://mlsanity.com/paper/2604.00283/

## Key facts

- No citing papers in the map yet (data through 14 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.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 20 of 20)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Your Diffusion Model is Secretly a Zero-Shot Classifier](https://mlsanity.com/paper/2303.16203/) (2023)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Denoising diffusion models for out-of-distribution detection](https://mlsanity.com/paper/2211.07740/) (2022)
- [DeepReach: A Deep Learning Approach to High-Dimensional Reachability](https://mlsanity.com/paper/2011.02082/) (2020)
- [Data-Driven Reachable Set Computation using Adaptive Gaussian Process Classification and Monte Carlo Methods](https://mlsanity.com/paper/1910.02500/) (2019)
- [Data-Driven Reachability Analysis from Noisy Data](https://mlsanity.com/paper/2105.07229/) (2021)
- [Data-Driven Reachability Analysis with Christoffel Functions](https://mlsanity.com/paper/2104.13902/) (2021)
- [Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inference](https://mlsanity.com/paper/2309.09187/) (2023)
- [Data-driven Reachability using Christoffel Functions and Conformal Prediction](https://mlsanity.com/paper/2309.08976/) (2023)
- [Statistical Reachability Analysis of Stochastic Cyber-Physical Systems under Distribution Shift](https://mlsanity.com/paper/2407.11609/) (2024)
- [Data-Driven Nonconvex Reachability Analysis using Exact Multiplication](https://mlsanity.com/paper/2504.02147/) (2025)
- [Scalable Data-Driven Reachability Analysis and Control via Koopman Operators with Conformal Coverage Guarantees](https://mlsanity.com/paper/2601.01076/) (2026)
- [Conformalized Data-Driven Reachability Analysis with PAC Guarantees](https://mlsanity.com/paper/2603.12220/) (2026)

## 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.