# Beyond One-Step Accuracy: State-Affine Latent Transition for Reliable Visual Planning

arXiv: https://arxiv.org/abs/2609.33595 · HTML: https://mlsanity.com/paper/2609.33595/

## 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 10 of its 41 references that are in the map.
- First posted on arXiv 27 Sep 2026.

## Placed in

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

## Builds on (most cited first, 10 of 10)

- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [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)
- [Combating the Compounding-Error Problem with a Multi-step Model](https://mlsanity.com/paper/1905.13320/) (2019)
- [What Drives Success in Physical Planning with Joint-Embedding Predictive World Models?](https://mlsanity.com/paper/2512.24497/) (2025)
- [Sensorimotor World Models: Perception for Action via Inverse Dynamics](https://mlsanity.com/paper/2606.20104/) (2026)
- [Sub-JEPA: Subspace Gaussian Regularization for Stable End-to-End World Models](https://mlsanity.com/paper/2605.09241/) (2026)
- [Subspace-Decomposed JEPAs: Disentangling Progression and Content in Latent World Models](https://mlsanity.com/paper/2605.31111/) (2026)
- [QQWorld: Quantile-Quantile Matching for World Model Regularization](https://mlsanity.com/paper/2607.28415/) (2026)

## Abstract (arXiv)

Joint-embedding world models enable visual planning by learning action-conditioned dynamics in latent space. Yet they are commonly trained for one-step prediction on encoded states, while planning recursively applies the learned transition to its own predictions. One-step accuracy therefore does not capture how prediction errors propagate under recursive rollout. We decompose multi-step rollout error into the errors introduced at individual steps and their propagation through subsequent transitions. We show that state-affine dynamics are precisely the differentiable transitions with state-independent Jacobians, eliminating the nonlinear propagation residual and making the error propagation operators depend only on the action sequence. Guided by this result, we introduce SALT (State-Affine Latent Transition), an action-conditioned state-affine dynamics model in which the action modulates both the state transformation and the additive update. We train SALT through recursive multi-step rollout supervision, feeding each predicted latent state back into the transition so that training matches how the model is used during planning. Across four visual planning environments, SALT exhibits 1.48--2.19× higher one-step prediction error than the matched LeWM baseline, yet improves closed-loop success in every environment by 10.0 percentage points on average. On OGBench-Cube, the fraction of episodes that fail with a sharp rise in model-predicted cost after execution decreases from 23.3% to 2.0%.