ODE-GS: Latent ODEs for Dynamic Scene Extrapolation with 3D Gaussian Splatting

We present ODE-GS, a novel method that unifies 3D Gaussian Splatting with latent neural ordinary differential equations (ODEs) to forecast dynamic 3D scenes far beyond the time span seen during training. Existing neural rendering systems - whether NeRF- or 3DGS-based - embed time directly in a deformation network and therefore excel at interpolation but collapse when asked to predict the future, where timestamps are strictly out-of-distribution. ODE-GS eliminates this dependency: after learning a high-fidelity, time-conditioned deformation model for the training window, we freeze it and train a Transformer encoder that summarizes past Gaussian trajectories into a latent state whose continuous evolution is governed by a neural ODE. Numerical integration of this latent flow yields smooth, physically plausible Gaussian trajectories that can be queried at any future instant and rendered in real time. Coupled with a variational objective and a lightweight second-derivative regularizer, ODE-GS attains state-of-the-art extrapolation on D-NeRF and NVFI benchmarks, improving PSNR by up to 10 dB and halving perceptual error (LPIPS) relative to the strongest baselines. Our results demonstrate that continuous-time latent dynamics are a powerful, practical route to photorealistic prediction of complex 3D scenes.