Latent world models plan by predicting how candidate actions advance learned latent dynamics. In self-predictive models, however, the encoder and predictor are optimized jointly and can co-adapt to latent transitions that are easy to predict but weakly constrained by the physical evolution of the scene. We introduce the cross-predictive JEPA (JEPA-x), which grounds latent dynamics in privileged physical trajectories. JEPA-x treats visual observations and physical states as corresponding views of the same action-conditioned trajectory, advances both through a shared predictor, and matches each prediction to the future representations of both modalities. This encourages the action-conditioned predictor to learn a common transition rule across the two views. Privileged physical state is used only during training, leaving a visual-only model at deployment. Empirical results show that JEPA-x reduces the rollout drift of a newly fitted predictor from $0.361$ to $0.104$ and increases mean control success from $53.6\%$ to $78.2\%$ on a multi-task suite spanning six evaluation subfamilies. We additionally show that direct physical-state regression improves decodability without improving forecastability or control, indicating that the benefit comes from shaping latent dynamics rather than merely encoding physical variables.

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