One Query, Real Motion: Local-Flow Distillation for Dynamic Gaussian Splatting

Dynamic 3D Gaussian Splatting methods usually represents a scene as canonical Gaussians deformed by a time-conditioned network. Such direct-query models enable real-time rendering, but formulate motion as a timestamp-to-state mapping rather than a state-to-state transition cause fast or complex motion is poorly constrained, which often produces motion blur and loss of fine spatial detail. To address this issue, we decompose motion into an exactly composable low-frequency positional semigroup and a state-dependent local flow that captures high-frequency residual dynamics. The local flow is learned through training-time rollouts supervised on keyframes and intermediate frames, and a transition-consistency objective distills the learned rollout dynamics into the direct decoder. At inference, only the direct decoder is used, so rendering remains a single-query operation, while the learned temporal dynamics improve alignment and detail. Experiments on HyperNeRF and N3DV demonstrate consistent improvements over baselines.