# Beyond Static Graph World Models: Learning Stochastic Latent Dynamics over Evolving Topologies

arXiv: https://arxiv.org/abs/2609.28670 · HTML: https://mlsanity.com/paper/2609.28670/

## 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 30 of its 46 references that are in the map.
- First posted on arXiv 23 Sep 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)

- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [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)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Vista: A Generalizable Driving World Model with High Fidelity and Versatile Controllability](https://mlsanity.com/paper/2405.17398/) (2024)
- [Navigation World Models](https://mlsanity.com/paper/2412.03572/) (2024)
- [Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data](https://mlsanity.com/paper/1605.06432/) (2016)
- [Foundations and modelling of dynamic networks using Dynamic Graph Neural Networks: A survey](https://mlsanity.com/paper/2005.07496/) (2020)
- [Probabilistic Recurrent State-Space Models](https://mlsanity.com/paper/1801.10395/) (2018)
- [Sparse Graph Attention Networks](https://mlsanity.com/paper/1912.00552/) (2019)
- [Efficient World Models with Context-Aware Tokenization](https://mlsanity.com/paper/2406.19320/) (2024)
- [Controlling Graph Dynamics with Reinforcement Learning and Graph Neural Networks](https://mlsanity.com/paper/2010.05313/) (2020)
- [SOLD: Slot Object-Centric Latent Dynamics Models for Relational Manipulation Learning from Pixels](https://mlsanity.com/paper/2410.08822/) (2024)
- [Graph World Model](https://mlsanity.com/paper/2507.10539/) (2025)
- [Learning Dynamic Attribute-factored World Models for Efficient Multi-object Reinforcement Learning](https://mlsanity.com/paper/2307.09205/) (2023)
- [Goal-directed graph construction using reinforcement learning](https://mlsanity.com/paper/2001.11279/) (2020)
- [Thinker: Learning to Plan and Act](https://mlsanity.com/paper/2307.14993/) (2023)
- [Exploring the limits of Hierarchical World Models in Reinforcement Learning](https://mlsanity.com/paper/2406.00483/) (2024)
- [Neural Motion Simulator: Pushing the Limit of World Models in Reinforcement Learning](https://mlsanity.com/paper/2504.07095/) (2025)
- [Hieros: Hierarchical Imagination on Structured State Space Sequence World Models](https://mlsanity.com/paper/2310.05167/) (2023)
- [Learning to Play Atari in a World of Tokens](https://mlsanity.com/paper/2406.01361/) (2024)
- [Graph World Models: Concepts, Taxonomy, and Future Directions](https://mlsanity.com/paper/2604.27895/) (2026)
- [Learn2Fold: Structured Origami Generation with World Model Planning](https://mlsanity.com/paper/2603.29585/) (2026)
- [Quantifying Multimodality in World Models](https://mlsanity.com/paper/2112.07263/) (2021)
- [Understanding Rollout Error in Graph World Models](https://mlsanity.com/paper/2606.27780/) (2026)
- [Multi-Agent Reinforcement Learning for Power Control in Wireless Networks via Adaptive Graphs](https://mlsanity.com/paper/2311.15858/) (2023)
- [STORI: A Benchmark and Taxonomy for Stochastic Environments](https://mlsanity.com/paper/2509.01793/) (2025)
- [Learning Ad Hoc Network Dynamics via Graph-Structured World Models](https://mlsanity.com/paper/2604.14811/) (2026)
- [A Structural Dynamics Graph World Model: Unified Modeling, Constrained Rollout, and Interpretable Calibration](https://mlsanity.com/paper/2608.08689/) (2026)

## Abstract (arXiv)

Graph-based world models have recently emerged as a means of learning transitions over relational state representations. However, existing approaches are largely limited to fixed-topology graphs or deterministic, fully observable environments. We propose the Graph Dynamics Model (GDM), a world model for graph-structured observations that is designed to handle the more general setting of evolving topologies in stochastic and partially observable environments. The GDM uses a sparse recurrent adjacency matrix to model topology updates and perform message passing, together with a recurrent state-space architecture for modelling stochastic transitions. Furthermore, we identify a gap in the evaluation of graph-based world models, as existing methods do not provide a means of comparing predicted and true distributions over the joint graph state comprising the interdependent topology, node features, and graph features. We therefore introduce the Graph Distribution Distance (GDD) metric, which uses maximum mean discrepancy with a graph kernel to comprehensively compare joint next-state distributions. We evaluate the GDM across several environments, including stochastic and partially observable settings. We demonstrate that GDM outperforms baseline models and displays zero-shot generalisation on large graphs.