4DGS-JEPA: Temporally Compositional Joint-Embedding Prediction for Dynamic Gaussian Splatting

Dynamic Gaussian Splatting explicitly represents evolving 3D scenes, but is typically optimized for reconstruction, rendering, or future-state generation rather than reusable predictive dynamics. We propose 4DGS-JEPA, a Gaussian-native joint-embedding predictive architecture for causal multi-horizon prediction. It combines hierarchical scene, motion-group, and Gaussian-level representations with a horizon-conditioned transition supporting both direct prediction and recursive rollout. Its central principle is temporal composition: different chronological transition paths reaching the same future endpoint should produce compatible predictive states. Endpoint and multi-horizon path supervision anchor predictions to future target embeddings, while a selective geometry decoder and geometry-level composition ground the learned dynamics in coherent group motion and Gaussian geometry without reconstructing complete future appearance. We further introduce hybrid correspondence that preserves reliable persistent canonical identity and applies residual optimal transport when correspondence becomes ambiguous under reordering or topology change. We theoretically characterize zero-loss path agreement and finite-error rollout accumulation. In controlled dynamic Gaussian worlds, temporal composition reduces direct–composed latent discrepancy by about 61% while slightly improving predictive accuracy, geometry-level composition reduces group-motion path discrepancy by about 72%, hybrid correspondence remains robust under reordering and topology change, and predicted Gaussian geometry can be rendered into held-out future frames without pixel-level training. These results establish 4DGS-JEPA as a predictive, temporally compositional formulation of dynamic Gaussian worlds.