Path Planning in Physically Viable World Models

World models for embodied AI must be physically viable: constructed to answer intervention queries by representing the physical structure governing action outcomes, rather than merely predicting future observations. Existing observation-predictive world models can produce visually plausible but physically wrong rollouts. This failure is structural; distinct physical systems can look identical yet diverge under intervention. We expose this problem with controlled benchmarks that fix the visible scene while varying latent physics. We show that such models may recommend infeasible actions, mispredict interaction outcomes, or certify unsafe behavior. We argue that embodied AI requires world models that identify the simplest physical abstraction sufficient to answer an intervention query. Such a model comprises modular components, including environment representation, latent state and parameter estimation, action specification, interventional dynamics, and query-level response. An autonomous orchestrator should identify the relevant abstraction and compose compatible learned and structured components per query. When closed-form physics is unavailable, uncertain, or costly, the transition model may be analytic, simulated, learned, or hybrid, but it must preserve the structure that determines interventional outcomes. This decomposition makes the model interpretable, its components verifiable, and its outputs auditable against the query. It also provides a design principle for new world models and a feasibility test for existing ones: the right abstraction is not the most detailed model of the world, but the simplest model that preserves the distinctions relevant to the query. We demonstrate this approach on queries that existing systems fail to answer correctly, and outline how an orchestrator can dynamically assemble and adapt physically viable models for planning, control, and verification.

Physically consistent motion planning remains a fundamental challenge in embodied AI, as generated trajectories must strictly conform to real-world execution dynamics. While latent world models offer a promising approach by predicting these dynamics, existing methods learn unconstrained future representations where absorbed physics remains implicit. Therefore, they fail to form reusable physical knowledge, which compromises reliability in unpredictable open-world navigation. To address this, we propose a novel Energy-Structured Latent World Model (ELWM). Our key idea is to structure the ELWM latent state to explicitly carry energy and momentum, ensuring strictly causal transitions via dissipation and control ports. Trained on multimodal RGB-D and inertial interaction histories, our model guarantees physically consistent predictions. We further implement this for motion planning by constructing Physics-Conditioned Neural Time Fields (PC-NTF), a key technical cornerstone that integrates ELWM into an arrival time field via the Eikonal equation to yield a physically-informed navigation policy. Across held-out scenes, our evaluation reveals significant improvements. Compared to generic latent models, PC-NTF reduces 0.8-s motion-prediction NRMSE from 0.36 to 0.29. Against Active Neural Time Fields, it improves navigation success from 81.3% to 89.7% and SPL from 0.64 to 0.73, while cutting the physical collision rate from 12.1% to 5.8% and the Eikonal residual from 0.083 to 0.031. Beyond these targeted gains, our results demonstrate that embedding explicit physical structures into latent spaces intrinsically bridges the gap between predictive world models and safe, dynamically feasible motion planning.

Different research lines use the term world model in different ways, yet they share a common aim: to capture how the world evolves under action in a form that supports perception, simulation, and planning. Two prominent realizations are neural predictors that learn dynamics in continuous vector spaces, and hand-built physics engines that expose explicit state and physical laws. Neural predictors scale from data but leave the form of the dynamics implicit; physics engines are inspectable and editable but difficult to construct at scale. We introduce VisualPatchWorld (VPW), which represents world dynamics as code. VPW first selects a qualitative dynamical form with short active probes, then fits that form's free parameters from recorded state-action traces by minimizing multi-step prediction error. The resulting programs can be rolled forward like a simulator, inspected in source form, and used inside model-predictive control; image-derived scene graphs can supply the live state at replan time. Across comparisons with prior code-based world models, VPW attains 69.0% mean planning success and exceeds the strongest code baseline by 23.5 points. The largest gains arise when choosing the correct qualitative dynamics is essential. Under the same planner, the induced models approach ground-truth engine success on navigation and grasp-rich control; a residual gap remains for contact-rich pushing, and checking a shortlist of promising plans in the engine closes most of that gap. These results establish a practical route toward automatically constructed code world models that are useful for planning. Code is available at https://github.com/HKBU-KnowComp/VisualPatchWorld/.