GP-4DGS: Probabilistic 4D Gaussian Splatting from Monocular Video via Variational Gaussian Processes

We present GP-4DGS, a probabilistic framework for monocular video reconstruction that models the motion of 4D Gaussian Splatting (GS) primitives using variational Gaussian Processes (GPs). In contrast to prior approaches that depend on manually designed motion priors, our kernel-based probabilistic formulation enables flexible, data-adaptive motion modeling while implicitly providing appropriate priors for unobserved regions. GP-4DGS employs variational GPs with spatial kernels to capture geometric correlations and periodic kernels to characterize temporal dynamics, achieving efficient scalability to large sets of primitives compared to standard GPs. To train GP-4DGS, we introduce an optimization strategy that jointly optimizes GS primitive parameters as well as GP hyperparameters, establishing a complementary relationship between probabilistic and geometric modeling. Beyond improved reconstruction quality, our variational GP formulation naturally supports uncertainty quantification and temporal extrapolation beyond the input sequence. Experiments on challenging dynamic scenes demonstrate that GP-4DGS delivers high-quality reconstructions, robustly handles severe occlusions and extreme viewpoints, and provides principled uncertainty estimation and extrapolation.