# Node-RF: Learning Generalized Continuous Space-Time Scene Dynamics with Neural ODE-based NeRFs

arXiv: https://arxiv.org/abs/2603.12078 · HTML: https://mlsanity.com/paper/2603.12078/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 33 references that are in the map.
- First posted on arXiv 12 Mar 2026.

## Builds on (most cited first, 24 of 24)

- [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)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [VBench: Comprehensive Benchmark Suite for Video Generative Models](https://mlsanity.com/paper/2311.17982/) (2023)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [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)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [Putting NeRF on a Diet: Semantically Consistent Few-Shot View Synthesis](https://mlsanity.com/paper/2104.00677/) (2021)
- [Fast Dynamic Radiance Fields with Time-Aware Neural Voxels](https://mlsanity.com/paper/2205.15285/) (2022)
- [X-CLIP: End-to-End Multi-grained Contrastive Learning for Video-Text Retrieval](https://mlsanity.com/paper/2207.07285/) (2022)
- [SimVP: Simpler yet Better Video Prediction](https://mlsanity.com/paper/2206.05099/) (2022)
- [Motion-aware 3D Gaussian Splatting for Efficient Dynamic Scene Reconstruction](https://mlsanity.com/paper/2403.11447/) (2024)
- [CNOS: A Strong Baseline for CAD-based Novel Object Segmentation](https://mlsanity.com/paper/2307.11067/) (2023)
- [Learning Smooth Neural Functions via Lipschitz Regularization](https://mlsanity.com/paper/2202.08345/) (2022)
- [MonoNeRF: Learning a Generalizable Dynamic Radiance Field from Monocular Videos](https://mlsanity.com/paper/2212.13056/) (2022)
- [MotionGS: Exploring Explicit Motion Guidance for Deformable 3D Gaussian Splatting](https://mlsanity.com/paper/2410.07707/) (2024)
- [Vid-ODE: Continuous-Time Video Generation with Neural Ordinary Differential Equation](https://mlsanity.com/paper/2010.08188/) (2020)
- [Neural Implicit Representations for Physical Parameter Inference from a Single Video](https://mlsanity.com/paper/2204.14030/) (2022)
- [Instant-NeRF: Instant On-Device Neural Radiance Field Training via Algorithm-Accelerator Co-Designed Near-Memory Processing](https://mlsanity.com/paper/2305.05766/) (2023)
- [Dynamic NeRF: A Review](https://mlsanity.com/paper/2405.08609/) (2024)

## Abstract (arXiv)

Predicting scene dynamics from visual observations is challenging. Existing methods capture dynamics only within observed boundaries failing to extrapolate far beyond the training sequence. Node-RF (Neural ODE-based NeRF) overcomes this limitation by integrating Neural Ordinary Differential Equations (NODEs) with dynamic Neural Radiance Fields (NeRFs), enabling a continuous-time, spatiotemporal representation that generalizes beyond observed trajectories at constant memory cost. From visual input, Node-RF learns an implicit scene state that evolves over time via an ODE solver, propagating feature embeddings via differential calculus. A NeRF-based renderer interprets calculated embeddings to synthesize arbitrary views for long-range extrapolation. Training on multiple motion sequences with shared dynamics allows for generalization to unseen conditions. Our experiments demonstrate that Node-RF can characterize abstract system behavior without explicit model to identify critical points for future predictions.