# Safety Certification in the Latent space using Control Barrier Functions and World Models

arXiv: https://arxiv.org/abs/2507.13871 · HTML: https://mlsanity.com/paper/2507.13871/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Latent dynamics models and model-based RL, one of 11 directions in World models.
- Builds on 22 of its 27 references that are in the map.
- First posted on arXiv 18 Jul 2025.

## Placed in

- World models / [Latent dynamics models and model-based RL](https://mlsanity.com/wm/latent-dynamics-models-and-model-based-rl/)

## Builds on (most cited first, 22 of 22)

- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [DINO-WM: World Models on Pre-trained Visual Features enable Zero-shot Planning](https://mlsanity.com/paper/2411.04983/) (2024)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [Learning for Safety-Critical Control with Control Barrier Functions](https://mlsanity.com/paper/1912.10099/) (2019)
- [Generalizing Safety Beyond Collision-Avoidance via Latent-Space Reachability Analysis](https://mlsanity.com/paper/2502.00935/) (2025)
- [Model-based Safe Deep Reinforcement Learning via a Constrained Proximal Policy Optimization Algorithm](https://mlsanity.com/paper/2210.07573/) (2022)
- [Formal Synthesis of Stochastic Systems via Control Barrier Certificates](https://mlsanity.com/paper/1905.04585/) (2019)
- [Control Barrier Functions for Unknown Nonlinear Systems using Gaussian Processes](https://mlsanity.com/paper/2010.05818/) (2020)
- [SABLAS: Learning Safe Control for Black-box Dynamical Systems](https://mlsanity.com/paper/2201.01918/) (2022)
- [Enforcing safety for vision-based controllers via Control Barrier Functions and Neural Radiance Fields](https://mlsanity.com/paper/2209.12266/) (2022)
- [A Physics-Informed Machine Learning Framework for Safe and Optimal Control of Autonomous Systems](https://mlsanity.com/paper/2502.11057/) (2025)
- [Learning a Formally Verified Control Barrier Function in Stochastic Environment](https://mlsanity.com/paper/2403.19332/) (2024)
- [Neural Control Barrier Functions for Safe Navigation](https://mlsanity.com/paper/2407.19907/) (2024)
- [Control Barrier Functions in Dynamic UAVs for Kinematic Obstacle Avoidance: A Collision Cone Approach](https://mlsanity.com/paper/2303.15871/) (2023)
- [Exact Imposition of Safety Boundary Conditions in Neural Reachable Tubes](https://mlsanity.com/paper/2404.00814/) (2024)
- [Semi-Supervised Safe Visuomotor Policy Synthesis using Barrier Certificates](https://mlsanity.com/paper/2409.12616/) (2024)
- [CP-NCBF: A Conformal Prediction-based Approach to Synthesize Verified Neural Control Barrier Functions](https://mlsanity.com/paper/2503.17395/) (2025)

## Built on by (most cited first, 2 of 2)

- [How to Train Your Latent Control Barrier Function: Smooth Safety Filtering Under Hard-to-Model Constraints](https://mlsanity.com/paper/2511.18606/) (2025)
- [Pixels to Proofs: Probabilistically-Safe Latent World Model Control via Parallel Conformal Robust MPC](https://mlsanity.com/paper/2606.15594/) (2026)

## Abstract (arXiv)

Synthesising safe controllers from visual data typically requires extensive supervised labelling of safety-critical data, which is often impractical in real-world settings. Recent advances in world models enable reliable prediction in latent spaces, opening new avenues for scalable and data-efficient safe control. In this work, we introduce a semi-supervised framework that leverages control barrier certificates (CBCs) learned in the latent space of a world model to synthesise safe visuomotor policies. Our approach jointly learns a neural barrier function and a safe controller using limited labelled data, while exploiting the predictive power of modern vision transformers for latent dynamics modelling.