# NODER: Image Sequence Regression Based on Neural Ordinary Differential Equations

arXiv: https://arxiv.org/abs/2407.13241 · HTML: https://mlsanity.com/paper/2407.13241/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 18 references that are in the map.
- First posted on arXiv 18 Jul 2024.

## Builds on (most cited first, 10 of 10)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Brain Imaging Generation with Latent Diffusion Models](https://mlsanity.com/paper/2209.07162/) (2022)
- [Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces](https://mlsanity.com/paper/1903.03545/) (2019)
- [Unsupervised Learning for Fast Probabilistic Diffeomorphic Registration](https://mlsanity.com/paper/1805.04605/) (2018)
- [Deforming Autoencoders: Unsupervised Disentangling of Shape and Appearance](https://mlsanity.com/paper/1806.06503/) (2018)
- [SADM: Sequence-Aware Diffusion Model for Longitudinal Medical Image Generation](https://mlsanity.com/paper/2212.08228/) (2022)
- [STAR-Transformer: A Spatio-temporal Cross Attention Transformer for Human Action Recognition](https://mlsanity.com/paper/2210.07503/) (2022)
- [Learning to synthesise the ageing brain without longitudinal data](https://mlsanity.com/paper/1912.02620/) (2019)
- [NODEO: A Neural Ordinary Differential Equation Based Optimization Framework for Deformable Image Registration](https://mlsanity.com/paper/2108.03443/) (2021)
- [Fast Predictive Simple Geodesic Regression](https://mlsanity.com/paper/1711.05766/) (2017)

## Built on by (most cited first, 6 of 6)

- [Temporal Flow Matching for Learning Spatio-Temporal Trajectories in 4D Longitudinal Medical Imaging](https://mlsanity.com/paper/2508.21580/) (2025)
- [TimeFlow: Temporal Conditioning for Longitudinal Brain MRI Registration and Aging Analysis](https://mlsanity.com/paper/2501.08667/) (2025)
- [Capturing Longitudinal Changes in Brain Morphology Using Temporally Parameterized Neural Displacement Fields](https://mlsanity.com/paper/2504.09514/) (2025)
- [ST-NeRP: Spatial-Temporal Neural Representation Learning with Prior Embedding for Patient-specific Imaging Study](https://mlsanity.com/paper/2410.19283/) (2024)
- [CRONOS: Continuous Time Reconstruction for 4D Medical Longitudinal Series](https://mlsanity.com/paper/2512.16577/) (2025)
- [Physics-Grounded Disentangled Flow Modeling for Brain Disease Progression Trajectory](https://mlsanity.com/paper/2606.28630/) (2026)

## Abstract (arXiv)

Regression on medical image sequences can capture temporal image pattern changes and predict images at missing or future time points. However, existing geodesic regression methods limit their regression performance by a strong underlying assumption of linear dynamics, while diffusion-based methods have high computational costs and lack constraints to preserve image topology. In this paper, we propose an optimization-based new framework called NODER, which leverages neural ordinary differential equations to capture complex underlying dynamics and reduces its high computational cost of handling high-dimensional image volumes by introducing the latent space. We compare our NODER with two recent regression methods, and the experimental results on ADNI and ACDC datasets demonstrate that our method achieves the state-of-the-art performance in 3D image regression. Our model needs only a couple of images in a sequence for prediction, which is practical, especially for clinical situations where extremely limited image time series are available for analysis. Our source code is available at https://github.com/ZedKing12138/NODER-pytorch.