# Energy-Structured Latent World Models with Neural Time Fields for Physically Constistent Open-World Motion Planning

arXiv: https://arxiv.org/abs/2608.09876 · HTML: https://mlsanity.com/paper/2608.09876/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 21 of its 50 references that are in the map.
- First posted on arXiv 10 Aug 2026.

## Placed in

- World models / [Latent predictive world models](https://mlsanity.com/wm/latent-predictive-world-models/)

## Builds on (most cited first, 21 of 21)

- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Habitat-Matterport 3D Dataset (HM3D): 1000 Large-scale 3D Environments for Embodied AI](https://mlsanity.com/paper/2109.08238/) (2021)
- [RMA: Rapid Motor Adaptation for Legged Robots](https://mlsanity.com/paper/2107.04034/) (2021)
- [World Action Models are Zero-shot Policies](https://mlsanity.com/paper/2602.15922/) (2026)
- [LeWorldModel: Stable End-to-End Joint-Embedding Predictive Architecture from Pixels](https://mlsanity.com/paper/2603.19312/) (2026)
- [LeJEPA: Provable and Scalable Self-Supervised Learning Without the Heuristics](https://mlsanity.com/paper/2511.08544/) (2025)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [iGibson 1.0: a Simulation Environment for Interactive Tasks in Large Realistic Scenes](https://mlsanity.com/paper/2012.02924/) (2020)
- [VL-JEPA: Joint Embedding Predictive Architecture for Vision-language](https://mlsanity.com/paper/2512.10942/) (2025)
- [Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems](https://mlsanity.com/paper/2107.08024/) (2021)
- [LaWAM: Latent World Action Models for Efficient Dynamics-Aware Robot Policies](https://mlsanity.com/paper/2606.15768/) (2026)
- [NTFields: Neural Time Fields for Physics-Informed Robot Motion Planning](https://mlsanity.com/paper/2210.00120/) (2022)
- [PIN-WM: Learning Physics-INformed World Models for Non-Prehensile Manipulation](https://mlsanity.com/paper/2504.16693/) (2025)
- [SkyJEPA: Learning Long-Horizon World Models for Zero-Shot Sim-to-Real Control of Quadrotors](https://mlsanity.com/paper/2606.23444/) (2026)
- [H-WM: Robotic Task and Motion Planning Guided by Hierarchical World Model](https://mlsanity.com/paper/2602.11291/) (2026)
- [Phys-JEPA: Physics-Informed Latent World Models for Multivariate Time-Series Forecasting](https://mlsanity.com/paper/2606.16076/) (2026)
- [PH-Dreamer: A Physics-Driven World Model via Port-Hamiltonian Generative Dynamics](https://mlsanity.com/paper/2605.18303/) (2026)
- [Physics-Informed Eikonal Caging for Whole-Arm Manipulation Planning](https://mlsanity.com/paper/2606.22143/) (2026)
- [CSympNet-ID: conformal-symplectic map learning for linearly damped Hamiltonian systems](https://mlsanity.com/paper/2607.03339/) (2026)

## Abstract (arXiv)

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.