# ATLAS: Aligned Transport of Latent Structure for Reliable World Model Planning

arXiv: https://arxiv.org/abs/2609.36333 · HTML: https://mlsanity.com/paper/2609.36333/

## 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 22 of its 28 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

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

## Builds on (most cited first, 22 of 22)

- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [Relational Knowledge Distillation](https://mlsanity.com/paper/1904.05068/) (2019)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [Revisiting Feature Prediction for Learning Visual Representations from Video](https://mlsanity.com/paper/2404.08471/) (2024)
- [Similarity-Preserving Knowledge Distillation](https://mlsanity.com/paper/1907.09682/) (2019)
- [TD-MPC2: Scalable, Robust World Models for Continuous Control](https://mlsanity.com/paper/2310.16828/) (2023)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [DINO-WM: World Models on Pre-trained Visual Features enable Zero-shot Planning](https://mlsanity.com/paper/2411.04983/) (2024)
- [Correlation Congruence for Knowledge Distillation](https://mlsanity.com/paper/1904.01802/) (2019)
- [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)
- [OGBench: Benchmarking Offline Goal-Conditioned RL](https://mlsanity.com/paper/2410.20092/) (2024)
- [Learning from Reward-Free Offline Data: A Case for Planning with Latent Dynamics Models](https://mlsanity.com/paper/2502.14819/) (2025)
- [Sliced-Wasserstein Autoencoder: An Embarrassingly Simple Generative Model](https://mlsanity.com/paper/1804.01947/) (2018)
- [stable-worldmodel: A Platform for Reproducible World Modeling Research and Evaluation](https://mlsanity.com/paper/2605.21800/) (2026)
- [Fast LeWorldModel](https://mlsanity.com/paper/2606.26217/) (2026)

## Abstract (arXiv)

Latent world models rely on representation geometry for planning, yet regularizing the latent marginal alone does not determine the state-to-state relationships used for action selection. We show that this can cause planning-relevant novelty structure to be weakened as representations are transformed into the final latent used by the planner. We introduce Aligned Transport of Latent Structure (ATLAS), a training objective that explicitly preserves relational geometry while calibrating the global latent distribution. ATLAS transfers normalized pairwise structure from an informative encoder representation to the planning latent and uses Wasserstein embedding matching (WEMReg) to calibrate its marginal through one-dimensional Wasserstein-2 transport. Our analysis shows that relational preservation and marginal calibration impose non-redundant constraints, and connects finite-candidate planning stability to relational distortion, latent-scale mismatch, and prediction error. Instantiated in LeWM, ATLAS improves mean goal-reaching success across PushT, TwoRoom, and OGBench-Cube on both lower- and higher-novelty evaluation subsets, with the largest gain on higher-novelty TwoRoom episodes. Representation and rollout diagnostics further show stronger novelty-related structure in the planning latent, improved marginal calibration, and lower multi-step prediction error. Together, these results highlight preservation of planning-relevant latent geometry as an important ingredient for reliable world-model planning. Code is available at https://anonymous.4open.science/r/atlas-world-model-72C4/.