4D Gaussian Splatting as a Learned Dynamical System

TL;DR

EvoGS reinterprets 4D Gaussian Splatting as a continuous-time neural dynamical system, enabling efficient learning, temporal extrapolation, and controllable scene synthesis for dynamic scenes.

Contribution

It introduces EvoGS, a novel approach modeling scene motion as a learned dynamical system, surpassing deformation-based methods in coherence and flexibility.

Findings

Better motion coherence and temporal consistency than deformation baselines

Enables real-time rendering of dynamic scenes

Supports temporal extrapolation and localized dynamics injection

Abstract

We reinterpret 4D Gaussian Splatting as a continuous-time dynamical system, where scene motion arises from integrating a learned neural dynamical field rather than applying per-frame deformations. This formulation, which we call EvoGS, treats the Gaussian representation as an evolving physical system whose state evolves continuously under a learned motion law. This unlocks capabilities absent in deformation-based approaches:(1) sample-efficient learning from sparse temporal supervision by modeling the underlying motion law; (2) temporal extrapolation enabling forward and backward prediction beyond observed time ranges; and (3) compositional dynamics that allow localized dynamics injection for controllable scene synthesis. Experiments on dynamic scene benchmarks show that EvoGS achieves better motion coherence and temporal consistency compared to deformation-field baselines while maintaining real-time rendering