# PH-Dreamer: A Physics-Driven World Model via Port-Hamiltonian Generative Dynamics

arXiv: https://arxiv.org/abs/2605.18303 · HTML: https://mlsanity.com/paper/2605.18303/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 30 of its 38 references that are in the map.
- First posted on arXiv 18 May 2026.

## Placed in

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

## Builds on (most cited first, 30 of 30)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [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)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [WorldSimBench: Towards Video Generation Models as World Simulators](https://mlsanity.com/paper/2410.18072/) (2024)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [VBench-2.0: Advancing Video Generation Benchmark Suite for Intrinsic Faithfulness](https://mlsanity.com/paper/2503.21755/) (2025)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [How Far is Video Generation from World Model: A Physical Law Perspective](https://mlsanity.com/paper/2411.02385/) (2024)
- [PhysGen: Rigid-Body Physics-Grounded Image-to-Video Generation](https://mlsanity.com/paper/2409.18964/) (2024)
- [Do generative video models understand physical principles?](https://mlsanity.com/paper/2501.09038/) (2025)
- [Hamiltonian Generative Networks](https://mlsanity.com/paper/1909.13789/) (2019)
- [Training Agents Inside of Scalable World Models](https://mlsanity.com/paper/2509.24527/) (2025)
- [Physics-Informed Diffusion Models](https://mlsanity.com/paper/2403.14404/) (2024)
- [STORM: Efficient Stochastic Transformer based World Models for Reinforcement Learning](https://mlsanity.com/paper/2310.09615/) (2023)
- [DreamerPro: Reconstruction-Free Model-Based Reinforcement Learning with Prototypical Representations](https://mlsanity.com/paper/2110.14565/) (2021)
- [Fast and Efficient Locomotion via Learned Gait Transitions](https://mlsanity.com/paper/2104.04644/) (2021)
- [SafeDreamer: Safe Reinforcement Learning with World Models](https://mlsanity.com/paper/2307.07176/) (2023)
- [RoboScape: Physics-informed Embodied World Model](https://mlsanity.com/paper/2506.23135/) (2025)
- [T2VPhysBench: A First-Principles Benchmark for Physical Consistency in Text-to-Video Generation](https://mlsanity.com/paper/2505.00337/) (2025)
- [SOLD: Slot Object-Centric Latent Dynamics Models for Relational Manipulation Learning from Pixels](https://mlsanity.com/paper/2410.08822/) (2024)
- [PIN-WM: Learning Physics-INformed World Models for Non-Prehensile Manipulation](https://mlsanity.com/paper/2504.16693/) (2025)
- [Learning Latent Dynamic Robust Representations for World Models](https://mlsanity.com/paper/2405.06263/) (2024)
- [Learning Physical Constraints with Neural Projections](https://mlsanity.com/paper/2006.12745/) (2020)
- [Physics-Informed Model-Based Reinforcement Learning](https://mlsanity.com/paper/2212.02179/) (2022)
- [Learning to Walk from Three Minutes of Real-World Data with Semi-structured Dynamics Models](https://mlsanity.com/paper/2410.09163/) (2024)
- [R2-Dreamer: Redundancy-Reduced World Models without Decoders or Augmentation](https://mlsanity.com/paper/2603.18202/) (2026)
- [Task Aware Dreamer for Task Generalization in Reinforcement Learning](https://mlsanity.com/paper/2303.05092/) (2023)
- [TransDreamerV3: Implanting Transformer In DreamerV3](https://mlsanity.com/paper/2506.17103/) (2025)

## Built on by (most cited first, 3 of 3)

- [Energy-Structured Latent World Models with Neural Time Fields for Physically Constistent Open-World Motion Planning](https://mlsanity.com/paper/2608.09876/) (2026)
- [Physis-Lang: Self-Evolving Language as a Physical Representation for Video World Model](https://mlsanity.com/paper/2609.40358/) (2026)
- [LeHami: Symplectic Latent Dynamics for World Models](https://mlsanity.com/paper/2610.15267/) (2026)

## Abstract (arXiv)

World models built on recurrent state space architectures enable efficient latent imagination, yet remain physically unstructured, producing dynamics that violate conservation and dissipative principles. We introduce a unified Port-Hamiltonian framework that remedies this through three synergistic mechanisms. First, we embed implicit physical priors into recurrent transitions by modeling projected latent evolution as action controlled energy routing governed by flow and dissipation, biasing the projected PH phase space toward a more compact and physically structured representation. Second, we develop a kinematics aware energy world model that estimates the Hamiltonian and power balance from proprioceptive observations, providing an explicit physical signal for thermodynamic reasoning. Third, leveraging these energy gradients, we establish an energy guided Actor-Critic that uses Lagrangian multipliers to regularize policy optimization toward lower energy and smoother control. Across visual control benchmarks, this paradigm not only attains superior asymptotic returns but also elevates internal simulator fidelity by establishing a tighter, lower variance alignment between imagined and real rewards, all while reducing latent phase space volume by 4.18-8.41%, energy consumption by up to 7.80%, and mean squared jerk by up to 9.38%.