# Temporal Flow Matching for Learning Spatio-Temporal Trajectories in 4D Longitudinal Medical Imaging

## TL;DR

This paper introduces Temporal Flow Matching (TFM), a novel generative method for modeling and predicting complex spatio-temporal trajectories in 4D longitudinal medical imaging, addressing limitations of existing approaches.

## Contribution

The paper presents TFM, a unified generative trajectory model capable of handling 3D volumes, multiple scans, and irregular sampling, surpassing existing methods in 4D medical image prediction.

## Key findings

- TFM outperforms existing spatio-temporal methods on three public datasets.
- Establishes a new state-of-the-art in 4D medical image prediction.
- Supports flexible sampling and multiple prior scans.

## Abstract

Understanding temporal dynamics in medical imaging is crucial for applications such as disease progression modeling, treatment planning and anatomical development tracking. However, most deep learning methods either consider only single temporal contexts, or focus on tasks like classification or regression, limiting their ability for fine-grained spatial predictions. While some approaches have been explored, they are often limited to single timepoints, specific diseases or have other technical restrictions. To address this fundamental gap, we introduce Temporal Flow Matching (TFM), a unified generative trajectory method that (i) aims to learn the underlying temporal distribution, (ii) by design can fall back to a nearest image predictor, i.e. predicting the last context image (LCI), as a special case, and (iii) supports $3D$ volumes, multiple prior scans, and irregular sampling. Extensive benchmarks on three public longitudinal datasets show that TFM consistently surpasses spatio-temporal methods from natural imaging, establishing a new state-of-the-art and robust baseline for $4D$ medical image prediction.