4DLoG: Generative modeling of neurodegenerative brain anatomy with 4D longitudinal diffusion model

Modeling and predicting neurodegenerative disease progression from medical images remains a major challenge in medical AI, with significant implications for early diagnosis, disease monitoring, and treatment planning. However, most longitudinal neuroimaging datasets are temporally sparse, with substantial gaps and missing follow-up scans for individual subjects. This makes it difficult to learn and accurately capture the continuous anatomical changes associated with disease progression at the level of individual subjects. To address this problem, we propose a novel model, named as 4DLoG, a full 4D (3D×T) Longitudinal Generative framework that effectively models and synthesizes follow-up brain anatomy over time, conditioned on available clinical and demographic variables. In contrast to previous approaches, our 4DLoG features two main contributions. First, it introduces a full 4D generative diffusion framework that jointly models spatial and temporal dependencies across complete longitudinal sequences through dedicated spatiotemporal attention, with robust spatial patch extraction and temporal alignment. Second, it explicitly learns the distribution of topology-preserving spatiotemporal deformations, which captures realistic geometric changes in brain structures over time. These new components enable a better generation of anatomically plausible future states from an imaging scan at any time point, providing greater flexibility for modeling individual longitudinal brain trajectories. We validate our model through both synthetic sequence generation and downstream longitudinal disease classification, as well as brain segmentation. Experiments on two large-scale longitudinal neuroimage datasets demonstrate that our method outperforms state-of-the-art baselines in generating anatomically accurate, temporally consistent, and clinically meaningful brain trajectories. Our code is available on Github.