Motion-MoE-GS: Decomposing Local Motion Laws for Dynamic 3D Gaussian Reconstruction

Complex object motion is locally coherent but globally heterogeneous: units subject to the same structural constraints, part relations, or interactions share a local motion law, while different regions can obey different laws. Existing dynamic 3D Gaussian methods commonly decode all primitive updates with one shared time-conditioned function. Conditioning this function on location, appearance, or a global dynamic state changes its input, but does not allocate different motion laws to different primitives. We propose Motion-MoE-GS, which casts dynamic 3D Gaussian reconstruction as conditional decomposition and allocation of local motion laws. The method evolves a continuous scene-level dynamic state with a Neural ODE and combines it with each Gaussian's static state to form a local motion descriptor. A motion-conditioned router sparsely selects two of four deformation experts. Each expert represents a learned local motion law and predicts position, rotation, and scale updates. Per-scene evaluations on NVFI-Obj and DynMultiParts support conditional motion-law decomposition as an effective inductive bias for heterogeneous 3D Gaussian dynamics.