Abstract Dynamic scene rendering has taken a leap forward with the rise of 4D Gaussian Splatting, but there is still one elusive challenge: how to make 3D Gaussians move through time as naturally as they would in the real world, all while keeping the motion smooth and consistent. In this paper, we present an approach that blends state‐space modeling with Wasserstein geometry, enabling a more fluid and coherent representation of dynamic scenes. We introduce a State Consistency Filter that merges prior predictions with the current observations, enabling Gaussians to maintain coherent trajectories over time. We also employ Wasserstein Consistency Constraint to ensure smooth, consistent updates of Gaussian parameters, reducing motion artifacts. Lastly, we leverage Wasserstein geometry to capture both translational motion and shape deformations, creating a more geometrically consistent model for dynamic scenes. Our approach models the evolution of Gaussians along geodesics on the manifold of Gaussian distributions, achieving smoother, more realistic motion and stronger temporal coherence. Experimental results show consistent improvements in rendering quality and efficiency. (see https://www.acm.org/publications/class-2012 )
Deng et al. (Sat,) studied this question.