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

arXiv: https://arxiv.org/abs/2506.05480 · HTML: https://mlsanity.com/paper/2506.05480/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 54 references that are in the map.
- First posted on arXiv 5 Jun 2025.

## Builds on (most cited first, 30 of 39)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstruction](https://mlsanity.com/paper/2309.13101/) (2023)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [Dynamic 3D Gaussians: Tracking by Persistent Dynamic View Synthesis](https://mlsanity.com/paper/2308.09713/) (2023)
- [Neural Body: Implicit Neural Representations with Structured Latent Codes for Novel View Synthesis of Dynamic Humans](https://mlsanity.com/paper/2012.15838/) (2020)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [Non-Rigid Neural Radiance Fields: Reconstruction and Novel View Synthesis of a Dynamic Scene From Monocular Video](https://mlsanity.com/paper/2012.12247/) (2020)
- [Dynamic View Synthesis from Dynamic Monocular Video](https://mlsanity.com/paper/2105.06468/) (2021)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Animatable Neural Radiance Fields for Modeling Dynamic Human Bodies](https://mlsanity.com/paper/2105.02872/) (2021)
- [SC-GS: Sparse-Controlled Gaussian Splatting for Editable Dynamic Scenes](https://mlsanity.com/paper/2312.14937/) (2023)
- [Fast Dynamic Radiance Fields with Time-Aware Neural Voxels](https://mlsanity.com/paper/2205.15285/) (2022)
- [Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis](https://mlsanity.com/paper/2312.16812/) (2023)
- [Neural Scene Graphs for Dynamic Scenes](https://mlsanity.com/paper/2011.10379/) (2020)
- [Neural Radiance Flow for 4D View Synthesis and Video Processing](https://mlsanity.com/paper/2012.09790/) (2020)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Tensor4D : Efficient Neural 4D Decomposition for High-fidelity Dynamic Reconstruction and Rendering](https://mlsanity.com/paper/2211.11610/) (2022)
- [4D-Rotor Gaussian Splatting: Towards Efficient Novel View Synthesis for Dynamic Scenes](https://mlsanity.com/paper/2402.03307/) (2024)
- [HyperReel: High-Fidelity 6-DoF Video with Ray-Conditioned Sampling](https://mlsanity.com/paper/2301.02238/) (2023)
- [NeRFPlayer: A Streamable Dynamic Scene Representation with Decomposed Neural Radiance Fields](https://mlsanity.com/paper/2210.15947/) (2022)
- [Learning Neural Volumetric Representations of Dynamic Humans in Minutes](https://mlsanity.com/paper/2302.12237/) (2023)

## Built on by (most cited first, 11 of 11)

- [Extending Foundational Monocular Depth Estimators to Fisheye Cameras with Calibration Tokens](https://mlsanity.com/paper/2508.04928/) (2025)
- [ETA: Energy-based Test-time Adaptation for Depth Completion](https://mlsanity.com/paper/2508.05989/) (2025)
- [Space-Time Forecasting of Dynamic Scenes with Motion-aware Gaussian Grouping](https://mlsanity.com/paper/2602.21668/) (2026)
- [Grow with the Flow: 4D Reconstruction of Growing Plants with Gaussian Flow Fields](https://mlsanity.com/paper/2602.08958/) (2026)
- [VisTa3D: A Dataset and Benchmark for Thin Object Reconstruction from Vision, Tactile, and 3D Point Clouds](https://mlsanity.com/paper/2608.20740/) (2026)
- [Gaussians on Fire: High-Frequency Reconstruction of Flames](https://mlsanity.com/paper/2511.22459/) (2025)
- [VeloGauss: Learning Physically Consistent Gaussian Velocity Fields from Videos](https://mlsanity.com/paper/2605.10567/) (2026)
- [Liquid Neural Networks as a Drop-in Continuous-Time Deformation Field for Dynamic 3D Gaussian Splatting](https://mlsanity.com/paper/2606.07670/) (2026)
- [Future Rendering neq Future Surface: A Benchmark and Dataset for Dynamic Surface Reconstruction Beyond the Observed Window](https://mlsanity.com/paper/2607.21471/) (2026)
- [Stochastic Liquid Deformation Fields: An SDE Generalisation of Closed-Form Continuous-Time Cells for Dynamic 3D Gaussian Splatting](https://mlsanity.com/paper/2608.28702/) (2026)
- [SurgGMF: Fully Causal Gaussian Motion Forecasting for Anticipatory Surgical Scene Rendering](https://mlsanity.com/paper/2609.34733/) (2026)

## Abstract (arXiv)

We introduce ODE-GS, a novel approach that integrates 3D Gaussian Splatting with latent neural ordinary differential equations (ODEs) to enable future extrapolation of dynamic 3D scenes. Unlike existing dynamic scene reconstruction methods, which rely on time-conditioned deformation networks and are limited to interpolation within a fixed time window, ODE-GS eliminates timestamp dependency by modeling Gaussian parameter trajectories as continuous-time latent dynamics. Our approach first learns an interpolation model to generate accurate Gaussian trajectories within the observed window, then trains a Transformer encoder to aggregate past trajectories into a latent state evolved via a neural ODE. Finally, numerical integration produces smooth, physically plausible future Gaussian trajectories, enabling rendering at arbitrary future timestamps. On the D-NeRF, NVFi, and HyperNeRF benchmarks, ODE-GS achieves state-of-the-art extrapolation performance, improving metrics by 19.8% compared to leading baselines, demonstrating its ability to accurately represent and predict 3D scene dynamics.