# Generalizing Safety Beyond Collision-Avoidance via Latent-Space Reachability Analysis

arXiv: https://arxiv.org/abs/2502.00935 · HTML: https://mlsanity.com/paper/2502.00935/

## Key facts

- Cited by 45 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 44 of its 58 references that are in the map.
- First posted on arXiv 2 Feb 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, 30 of 44)

- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Mastering Atari with Discrete World Models](https://mlsanity.com/paper/2010.02193/) (2020)
- [Recurrent World Models Facilitate Policy Evolution](https://mlsanity.com/paper/1809.01999/) (2018)
- [DayDreamer: World Models for Physical Robot Learning](https://mlsanity.com/paper/2206.14176/) (2022)
- [Temporal Difference Learning for Model Predictive Control](https://mlsanity.com/paper/2203.04955/) (2022)
- [Universal Manipulation Interface: In-The-Wild Robot Teaching Without In-The-Wild Robots](https://mlsanity.com/paper/2402.10329/) (2024)
- [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)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [Recovery RL: Safe Reinforcement Learning with Learned Recovery Zones](https://mlsanity.com/paper/2010.15920/) (2020)
- [Structured World Models from Human Videos](https://mlsanity.com/paper/2308.10901/) (2023)
- [Learning to be Safe: Deep RL with a Safety Critic](https://mlsanity.com/paper/2010.14603/) (2020)
- [Learning Control Barrier Functions from Expert Demonstrations](https://mlsanity.com/paper/2004.03315/) (2020)
- [DeepReach: A Deep Learning Approach to High-Dimensional Reachability](https://mlsanity.com/paper/2011.02082/) (2020)
- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [Agile But Safe: Learning Collision-Free High-Speed Legged Locomotion](https://mlsanity.com/paper/2401.17583/) (2024)
- [Safety and Liveness Guarantees through Reach-Avoid Reinforcement Learning](https://mlsanity.com/paper/2112.12288/) (2021)
- [Reach-Avoid Problems with Time-Varying Dynamics, Targets and Constraints](https://mlsanity.com/paper/1410.6445/) (2014)
- [Robot Motion Planning in Learned Latent Spaces](https://mlsanity.com/paper/1807.10366/) (2018)
- [Model-Based Runtime Monitoring with Interactive Imitation Learning](https://mlsanity.com/paper/2310.17552/) (2023)
- [Multi-Task Interactive Robot Fleet Learning with Visual World Models](https://mlsanity.com/paper/2410.22689/) (2024)
- [Maximum Likelihood Constraint Inference for Inverse Reinforcement Learning](https://mlsanity.com/paper/1909.05477/) (2019)
- [ISAACS: Iterative Soft Adversarial Actor-Critic for Safety](https://mlsanity.com/paper/2212.03228/) (2022)
- [Sim-to-Lab-to-Real: Safe Reinforcement Learning with Shielding and Generalization Guarantees](https://mlsanity.com/paper/2201.08355/) (2022)
- [Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations](https://mlsanity.com/paper/2111.09971/) (2021)
- [Learning Safety Constraints from Demonstrations with Unknown Rewards](https://mlsanity.com/paper/2305.16147/) (2023)

## Built on by (most cited first, 30 of 45)

- [DynaGuide: Steering Diffusion Polices with Active Dynamic Guidance](https://mlsanity.com/paper/2506.13922/) (2025)
- [Uncertainty-aware Latent Safety Filters for Avoiding Out-of-Distribution Failures](https://mlsanity.com/paper/2505.00779/) (2025)
- [PlayWorld: Learning Robot World Models from Autonomous Play](https://mlsanity.com/paper/2603.09030/) (2026)
- [Foundational World Models Accurately Detect Bimanual Manipulator Failures](https://mlsanity.com/paper/2603.06987/) (2026)
- [Preemptive Detection and Steering of LLM Misalignment via Latent Reachability](https://mlsanity.com/paper/2509.21528/) (2025)
- [MoE-DP: An MoE-Enhanced Diffusion Policy for Robust Long-Horizon Robotic Manipulation with Skill Decomposition and Failure Recovery](https://mlsanity.com/paper/2511.05007/) (2025)
- [LIBERO-Safety: A Comprehensive Benchmark for Physical and Semantic Safety in Vision-Language-Action Models](https://mlsanity.com/paper/2606.23686/) (2026)
- [WoMAP: World Models For Embodied Open-Vocabulary Object Localization](https://mlsanity.com/paper/2506.01600/) (2025)
- [How to Train Your Latent Control Barrier Function: Smooth Safety Filtering Under Hard-to-Model Constraints](https://mlsanity.com/paper/2511.18606/) (2025)
- [AnySafe: Adapting Latent Safety Filters at Runtime via Safety Constraint Parameterization in the Latent Space](https://mlsanity.com/paper/2509.19555/) (2025)
- [Learning Conservative Neural Control Barrier Functions from Offline Data](https://mlsanity.com/paper/2505.00908/) (2025)
- [Designing Latent Safety Filters using Pre-Trained Vision Models](https://mlsanity.com/paper/2509.14758/) (2025)
- [Biased Dreams: Limitations to Epistemic Uncertainty Quantification in Latent Dynamics Models](https://mlsanity.com/paper/2604.25416/) (2026)
- [Statistically Assuring Safety of Control Systems using Ensembles of Safety Filters and Conformal Prediction](https://mlsanity.com/paper/2511.07899/) (2025)
- [Pixels to Proofs: Probabilistically-Safe Latent World Model Control via Parallel Conformal Robust MPC](https://mlsanity.com/paper/2606.15594/) (2026)
- [Pretrained Embeddings as a Behavior Specification Mechanism](https://mlsanity.com/paper/2503.02012/) (2025)
- [Provably Optimal Reinforcement Learning under Safety Filtering](https://mlsanity.com/paper/2510.18082/) (2025)
- [Safety Certification in the Latent space using Control Barrier Functions and World Models](https://mlsanity.com/paper/2507.13871/) (2025)
- [GenCtrl -- A Formal Controllability Toolkit for Generative Models](https://mlsanity.com/paper/2601.05637/) (2026)
- [Safe Control using Learned Safety Filters and Adaptive Conformal Inference](https://mlsanity.com/paper/2604.18482/) (2026)
- [How Well Do Latent World Models Understand Partially Observable Safety Constraints?](https://mlsanity.com/paper/2510.06492/) (2025)
- [From Refusal to Recovery: A Control-Theoretic Approach to Generative AI Guardrails](https://mlsanity.com/paper/2510.13727/) (2025)
- [Learning Neural Control Barrier Functions from Expert Demonstrations using Inverse Constraint Learning](https://mlsanity.com/paper/2510.21560/) (2025)
- [Verification of Unknown Dynamical Systems via Autoencoder Latent Space](https://mlsanity.com/paper/2512.13593/) (2025)
- [CMP: Robust Whole-Body Tracking for Loco-Manipulation via Competence Manifold Projection](https://mlsanity.com/paper/2604.07457/) (2026)
- [Latent Q-Barrier Shielding for Safe In-Context Reinforcement Learning](https://mlsanity.com/paper/2605.25267/) (2026)
- [StressDream: Steering Video World Models for Robust Policy Evaluation and Improvement](https://mlsanity.com/paper/2606.00267/) (2026)
- [Permissive Safety Through Trusted Inference: Verifiable Belief-Space Neural Safety Filters for Assured Interactive Robotics](https://mlsanity.com/paper/2606.02562/) (2026)
- [Towards General Language-Conditioned Latent Safety Filters](https://mlsanity.com/paper/2608.00315/) (2026)
- [V-MORALS: Visual Morse Graph-Aided Estimation of Regions of Attraction in a Learned Latent Space](https://mlsanity.com/paper/2602.23524/) (2026)

## Abstract (arXiv)

Hamilton-Jacobi (HJ) reachability is a rigorous mathematical framework that enables robots to simultaneously detect unsafe states and generate actions that prevent future failures. While in theory, HJ reachability can synthesize safe controllers for nonlinear systems and nonconvex constraints, in practice, it has been limited to hand-engineered collision-avoidance constraints modeled via low-dimensional state-space representations and first-principles dynamics. In this work, our goal is to generalize safe robot controllers to prevent failures that are hard--if not impossible--to write down by hand, but can be intuitively identified from high-dimensional observations: for example, spilling the contents of a bag. We propose Latent Safety Filters, a latent-space generalization of HJ reachability that tractably operates directly on raw observation data (e.g., RGB images) to automatically compute safety-preserving actions without explicit recovery demonstrations by performing safety analysis in the latent embedding space of a generative world model. Our method leverages diverse robot observation-action data of varying quality (including successes, random exploration, and unsafe demonstrations) to learn a world model. Constraint specification is then transformed into a classification problem in the latent space of the learned world model. In simulation and hardware experiments, we compute an approximation of Latent Safety Filters to safeguard arbitrary policies (from imitation- learned policies to direct teleoperation) from complex safety hazards, like preventing a Franka Research 3 manipulator from spilling the contents of a bag or toppling cluttered objects.