PUGS: Physics-Guided Uncertainty Modeling for Dynamic 3D Gaussian Splatting in Underwater Scenes

Dynamic 3D Gaussian Splatting (3DGS) has recently emerged as an efficient paradigm for reconstructing dynamic scenes. Existing approaches predominantly model scene dynamics through deterministic deformation fields, implicitly assuming that each Gaussian follows a unique geometric trajectory over time. However, this assumption fundamentally breaks down in underwater scenes, where light scattering, refraction, marine snow, and severe visibility degradation introduce substantial physical ambiguity into the imaging process. In this paper, we present a physics-guided uncertainty model for underwater dynamic 3D Gaussian Splatting that learns to detect the inherent uncertainty induced by underwater image formation and exploits it as a physical signal to guide dynamic scene representation. Instead of estimating a single deterministic displacement, PUGS parameterizes each Gaussian's motion as a probability distribution characterized by both its expected deformation and physical uncertainty. This probabilistic formulation enables the model to distinguish stable structural evolution from stochastic optical perturbations caused by underwater media. Based on this representation, we introduce a stochastic deformation optimization strategy that samples Gaussian trajectories through local reparameterization, encouraging adaptive exploration of multiple physically plausible solutions during training. To progressively consolidate the learned geometry, we further propose an uncertainty annealing framework together with a dual-path self-consistency distillation objective, which gradually transforms stochastic exploration into deterministic reconstruction while preserving temporal coherence. Furthermore, the learned uncertainty naturally serves as a physical reliability indicator: it guides adaptive Gaussian densification, concentrating model capacity on regions where scattering and optical degradation most severely degrade visual information. Extensive experiments on challenging underwater dynamic datasets and physics-aware benchmark demonstrate that the proposed method consistently outperforms state-of-the-art methods in rendering quality, temporal consistency, and reconstruction robustness under complex conditions.