# World Models with Predictable Long-Horizon Marginals

arXiv: https://arxiv.org/abs/2609.32657 · HTML: https://mlsanity.com/paper/2609.32657/

## 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 2 of its 37 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Placed in

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

## Builds on (most cited first, 2 of 2)

- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport](https://mlsanity.com/paper/1903.03704/) (2019)

## Abstract (arXiv)

Accurate one-step predictions do not ensure that a world model's rollouts retain the data distribution. We make the model's decoded stationary law explicit by learning a decoder of a fixed Gaussian reference and constraining the behaviour-averaged transition to preserve that reference. For controlled systems, a joint transition uses a conditional action chart to preserve behaviour occupancy without requiring invariance at each fixed action. Joint state--action rotations and parallel Gaussian noise give an exactly preserving transition with a tractable conditional density. We derive an absolute convergence bound from finite initialization banks and control departure from the reference through conditional action-space divergence. Across 216 fitted pixel checkpoints on twelve control tasks, the occupancy model with a reference mixture retains every evaluated chain at 105 steps in all 36 task--seed cells, with a rollout-minus-reference energy-statistic difference of -0.0002±0.0003 (training-seed standard error). Each of the four nonpreserving comparison arms loses chains, although the Gaussian arm is more accurate at ten steps. An offline DreamerV3 reference also achieves better short-horizon accuracy. These results distinguish three properties of a world model: the distribution it approaches, the rate of approach, and the conditional dynamics it learns.