# QQWorld: Quantile-Quantile Matching for World Model Regularization

arXiv: https://arxiv.org/abs/2607.28415 · HTML: https://mlsanity.com/paper/2607.28415/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 25 of its 35 references that are in the map.
- First posted on arXiv 30 Jul 2026.

## Placed in

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

## Builds on (most cited first, 25 of 25)

- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [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)
- [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)
- [DINO-WM: World Models on Pre-trained Visual Features enable Zero-shot Planning](https://mlsanity.com/paper/2411.04983/) (2024)
- [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)
- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [Learning from Reward-Free Offline Data: A Case for Planning with Latent Dynamics Models](https://mlsanity.com/paper/2502.14819/) (2025)
- [LaWAM: Latent World Action Models for Efficient Dynamics-Aware Robot Policies](https://mlsanity.com/paper/2606.15768/) (2026)
- [Hierarchical Planning with Latent World Models](https://mlsanity.com/paper/2604.03208/) (2026)
- [Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distances](https://mlsanity.com/paper/2210.09160/) (2022)
- [Interpreting Physics in Video World Models](https://mlsanity.com/paper/2602.07050/) (2026)
- [Sensorimotor World Models: Perception for Action via Inverse Dynamics](https://mlsanity.com/paper/2606.20104/) (2026)
- [A Two-Sample Conditional Distribution Test Using Conformal Prediction and Weighted Rank Sum](https://mlsanity.com/paper/2010.07147/) (2020)
- [Sub-JEPA: Subspace Gaussian Regularization for Stable End-to-End World Models](https://mlsanity.com/paper/2605.09241/) (2026)
- [VISReg: Variance-Invariance-Sketching Regularization for JEPA training](https://mlsanity.com/paper/2606.02572/) (2026)
- [Latent Geometry Beyond Search: Amortizing Planning in World Models](https://mlsanity.com/paper/2605.08732/) (2026)
- [Closed-form Expressions for Maximum Mean Discrepancy with Applications to Wasserstein Auto-Encoders](https://mlsanity.com/paper/1901.03227/) (2019)
- [Subspace-Decomposed JEPAs: Disentangling Progression and Content in Latent World Models](https://mlsanity.com/paper/2605.31111/) (2026)
- [FF-JEPA: Long-Horizon Planning in World Models with Latent Planners](https://mlsanity.com/paper/2606.09311/) (2026)
- [A Generalization Theory for JEPA-Based World Models](https://mlsanity.com/paper/2606.27014/) (2026)
- [IMWM: Intuition Models Complement World Models for Latent Planning](https://mlsanity.com/paper/2606.01626/) (2026)

## Built on by (most cited first, 5 of 5)

- [PhyLatent: Learning Dynamics-Relevant Representations for JEPA World Models](https://mlsanity.com/paper/2608.05720/) (2026)
- [Spectral-Target Physical Latent Structuring for JEPA-Style World Models](https://mlsanity.com/paper/2609.04264/) (2026)
- [Beyond One-Step Accuracy: State-Affine Latent Transition for Reliable Visual Planning](https://mlsanity.com/paper/2609.33595/) (2026)
- [Learning to Plan from Random Exploration](https://mlsanity.com/paper/2609.38383/) (2026)
- [Shared Gaussianization: What Gaussian Regularizers Certify About Contrastive Learning, and What They Miss](https://mlsanity.com/paper/2610.10299/) (2026)

## Abstract (arXiv)

Latent world models enable efficient planning by predicting future states in a compact representation space, but their performance depends critically on the quality of the learned latent distribution. LeWorldModel (LeWM) regularizes its latents toward an isotropic Gaussian using the Epps-Pulley (EP) objective. We show that the corrective gradients of EP rapidly vanish for isolated tail samples, leaving heavy-tailed deviations insufficiently controlled. To address this limitation, we propose QQWorld, which replaces EP with a quantile-quantile matching objective that directly aligns projected latent samples with rank-matched Gaussian quantiles, thereby maintaining effective corrective gradients in the tails. We further develop cross-batch QQ, which enlarges the effective ranking pool using detached samples from previous batches, and characterize its bias-variance trade-off. Across four control environments, QQWorld effectively improves the average planning success rate of LeWM, while consistently yielding better Gaussian alignment and thinner latent tails.