# Cloning Deterministic Worlds: The Critical Role of Latent Geometry in Long-Horizon World Models

arXiv: https://arxiv.org/abs/2510.26782 · HTML: https://mlsanity.com/paper/2510.26782/

## 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 63 of its 85 references that are in the map.
- First posted on arXiv 30 Oct 2025.

## Placed in

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

## Builds on (most cited first, 30 of 63)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Genie: Generative Interactive Environments](https://mlsanity.com/paper/2402.15391/) (2024)
- [Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think](https://mlsanity.com/paper/2410.06940/) (2024)
- [Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusion](https://mlsanity.com/paper/2407.01392/) (2024)
- [Self Forcing: Bridging the Train-Test Gap in Autoregressive Video Diffusion](https://mlsanity.com/paper/2506.08009/) (2025)
- [Time-Contrastive Networks: Self-Supervised Learning from Video](https://mlsanity.com/paper/1704.06888/) (2017)
- [From Slow Bidirectional to Fast Autoregressive Video Diffusion Models](https://mlsanity.com/paper/2412.07772/) (2024)
- [DINO-WM: World Models on Pre-trained Visual Features enable Zero-shot Planning](https://mlsanity.com/paper/2411.04983/) (2024)
- [Spatiotemporal Contrastive Video Representation Learning](https://mlsanity.com/paper/2008.03800/) (2020)
- [WorldVLA: Towards Autoregressive Action World Model](https://mlsanity.com/paper/2506.21539/) (2025)
- [Diffusion for World Modeling: Visual Details Matter in Atari](https://mlsanity.com/paper/2405.12399/) (2024)
- [Improving Sample Efficiency in Model-Free Reinforcement Learning from Images](https://mlsanity.com/paper/1910.01741/) (2019)
- [Deep Compression Autoencoder for Efficient High-Resolution Diffusion Models](https://mlsanity.com/paper/2410.10733/) (2024)
- [How Far is Video Generation from World Model: A Physical Law Perspective](https://mlsanity.com/paper/2411.02385/) (2024)
- [Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/1901.07821/) (2019)
- [Matrix-game 2.0: An open-source real-time and streaming interactive world model](https://mlsanity.com/paper/2508.13009/) (2025)
- [DreamGen: Unlocking Generalization in Robot Learning through Video World Models](https://mlsanity.com/paper/2505.12705/) (2025)

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

- [RAE-NWM: Navigation World Model in Dense Visual Representation Space](https://mlsanity.com/paper/2603.09241/) (2026)
- [Beyond Myopic World Models: Long-Horizon End-to-End Training for Direct Future Prediction](https://mlsanity.com/paper/2608.07420/) (2026)
- [DashVMC: Real-Time Discrete World Model Control in Geometry Dash](https://mlsanity.com/paper/2609.40003/) (2026)

## Abstract (arXiv)

A world model is an internal model that simulates how the world evolves. Given past observations and actions, it predicts the future physical state of both the embodied agent and its environment. Accurate world models are essential for enabling agents to think, plan, and reason effectively in complex, dynamic settings. However, existing world models often focus on random generation of open worlds, but neglect the need for high-fidelity modeling of deterministic scenarios (such as fixed-map mazes and static space robot navigation). In this work, we take a step toward building a truly accurate world model by addressing a fundamental yet open problem: constructing a model that can fully clone a deterministic 3D world. 1) Through diagnostic experiment, we quantitatively demonstrate that high-fidelity cloning is feasible and the primary bottleneck for long-horizon fidelity is the geometric structure of the latent representation, not the dynamics model itself. 2) Building on this insight, we show that applying temporal contrastive learning principle as a geometric regularization can effectively curate a latent space that better reflects the underlying physical state manifold, demonstrating that contrastive constraints can serve as a powerful inductive bias for stable world modeling; we call this approach Geometrically-Regularized World Models (GRWM). At its core is a lightweight geometric regularization module that can be seamlessly integrated into standard autoencoders, reshaping their latent space to provide a stable foundation for effective dynamics modeling. By focusing on representation quality, GRWM offers a simple yet powerful pipeline for improving world model fidelity.