EvoGS: 4D Gaussian Splatting as a Learned Dynamical System

Arnold Caleb Asiimwe1, Carl Vondrick2
1Princeton University
2Columbia University

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.

EvoGS Teaser Figure
EvoGS learns to model dynamic scenes as continuous evolution functions.

Sparse Temporal Reconstruction

EvoGS learns smooth motion from sparse temporal supervision — training on only a subset of frames (e.g., every 3rd frame) yet faithfully reconstructing the full continuous evolution. Explore the 3D point cloud at different timepoints.

cut_roasted_beef — trained on every 3rd frame, 217K Gaussians rendered in real-time.

Temporal Extrapolation

By learning a continuous velocity field, EvoGS can predict beyond observed frames. The model is trained only on the first half of the sequence (t ≤ 0.50) and extrapolates into the unseen future. Compare observed vs. predicted timepoints below.

cut_roasted_beef — trained on t ∈ [0, 0.50], extrapolated to t = 0.75. ✅ observed, 🔮 predicted.

Dynamics Injection

Because EvoGS represents motion as a continuous velocity field, we can inject, mix, or replace portions of the flow in specific scene regions without retraining — enabling compositional scene editing and localized motion synthesis.

cut_roasted_beef — localized dynamics injection demonstrating compositional scene editing.

Citation

@article{asiimwe2025evogs,
  title={EvoGS: 4D Gaussian Splatting as a Learned Dynamical System},
  author={Asiimwe, Arnold Caleb and Vondrick, Carl},
  journal={arXiv preprint arXiv:2025},
  year={2025}
}