We present GP-4DGS, a novel framework that integrates Gaussian Processes (GPs) into 4D Gaussian Splatting (4DGS) for principled probabilistic modeling of dynamic scenes. While existing 4DGS methods focus on deterministic reconstruction, they are inherently limited in capturing motion ambiguity and lack mechanisms to assess prediction reliability. By leveraging the kernel-based probabilistic nature of GPs, our approach introduces three key capabilities: (i) uncertainty quantification for motion predictions, (ii) motion estimation for unobserved or sparsely sampled regions, and (iii) temporal extrapolation beyond observed training frames. To scale GPs to the large number of Gaussian primitives in 4DGS, we design spatio-temporal kernels that capture the correlation structure of deformation fields and adopt variational Gaussian Processes with inducing points for tractable inference. Our experiments show that GP-4DGS enhances reconstruction quality while providing reliable uncertainty estimates that effectively identify regions of high motion ambiguity. By addressing these challenges, our work takes a meaningful step toward bridging probabilistic modeling and neural graphics.

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