# ODeform: Learning Continuous 4D Motion for Shape Deformation with Neural ODEs

arXiv: https://arxiv.org/abs/2607.20670 · HTML: https://mlsanity.com/paper/2607.20670/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 31 references that are in the map.
- First posted on arXiv 22 Jul 2026.

## Builds on (most cited first, 19 of 19)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [FlowNet3D: Learning Scene Flow in 3D Point Clouds](https://mlsanity.com/paper/1806.01411/) (2018)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [MeteorNet: Deep Learning on Dynamic 3D Point Cloud Sequences](https://mlsanity.com/paper/1910.09165/) (2019)
- [Auxiliary Tasks in Multi-task Learning](https://mlsanity.com/paper/1805.06334/) (2018)
- [Neural Flows: Efficient Alternative to Neural ODEs](https://mlsanity.com/paper/2110.13040/) (2021)
- [TACTO: A Fast, Flexible, and Open-source Simulator for High-Resolution Vision-based Tactile Sensors](https://mlsanity.com/paper/2012.08456/) (2020)
- [Robot See Robot Do: Imitating Articulated Object Manipulation with Monocular 4D Reconstruction](https://mlsanity.com/paper/2409.18121/) (2024)
- [HouseCat6D -- A Large-Scale Multi-Modal Category Level 6D Object Perception Dataset with Household Objects in Realistic Scenarios](https://mlsanity.com/paper/2212.10428/) (2022)
- [CaSPR: Learning Canonical Spatiotemporal Point Cloud Representations](https://mlsanity.com/paper/2008.02792/) (2020)
- [Deformation and Correspondence Aware Unsupervised Synthetic-to-Real Scene Flow Estimation for Point Clouds](https://mlsanity.com/paper/2203.16895/) (2022)
- [Neural Implicit Representations for Physical Parameter Inference from a Single Video](https://mlsanity.com/paper/2204.14030/) (2022)
- [Data-Free Learning of Reduced-Order Kinematics](https://mlsanity.com/paper/2305.03846/) (2023)
- [Neural Eulerian Scene Flow Fields](https://mlsanity.com/paper/2410.02031/) (2024)
- [Modulated Neural ODEs](https://mlsanity.com/paper/2302.13262/) (2023)
- [Dynamic Hyperbolic Attention Network for Fine Hand-object Reconstruction](https://mlsanity.com/paper/2309.02965/) (2023)
- [3D-PhysNet: Learning the Intuitive Physics of Non-Rigid Object Deformations](https://mlsanity.com/paper/1805.00328/) (2018)
- [Physics-Encoded Graph Neural Networks for Deformation Prediction under Contact](https://mlsanity.com/paper/2402.03466/) (2024)

## Abstract (arXiv)

Modeling continuous object deformation is important for many computer vision and robotics tasks, such as manipulation and simulation. Existing approaches rely on learning-based methods or physics simulators to model shape deformations. However, these approaches either use discrete time steps or are too computationally intensive for real-time applications. We present ODeform, a novel extension of Neural Ordinary Differential Equations to continuous 4D dynamics of deformable objects in 3D space. Our method transforms 3D point clouds and physical conditions (like material properties) into a unified latent space. By solving the resulting ordinary differential equations over time, we model deformations as continuous flows within this learned embedding, eliminating the need for discrete time steps while maintaining computational efficiency. We evaluate our approach on unseen physical parameter configurations, showing improved motion prediction accuracy over baseline methods. Our experiments further demonstrate a successful transfer to real 3D captured objects with novel shapes, along with effective interpolation and extrapolation of the learned dynamics. Our code and data will be made publicly available.