Not yet reviewed by Pith; the record is open.

Accurate forecasting of individualized, high-resolution cortical thickness (CTh) trajectories is essential for detecting subtle cortical changes, providing invaluable insights into neurodegenerative processes and facilitating earlier and more precise intervention strategies. However, CTh forecasting is a challenging task due to the intricate non-Euclidean geometry of the cerebral cortex and the need to integrate multi-modal data for subject-specific predictions. To address these challenges, we introduce the Spherical Brownian Bridge Diffusion Model (SBDM). Specifically, we propose a bidirectional conditional Brownian bridge diffusion process to forecast CTh trajectories at the vertex level of registered cortical surfaces. Our technical contribution includes a new denoising model, the conditional spherical U-Net (CoS-UNet), which combines spherical convolutions and dense cross-attention to integrate cortical surfaces and tabular conditions seamlessly. Compared to previous approaches, SBDM achieves significantly reduced prediction errors, as demonstrated by our experiments based on longitudinal datasets from the ADNI and OASIS. Additionally, we demonstrate SBDM's ability to generate individual factual and counterfactual CTh trajectories, offering a novel framework for exploring hypothetical scenarios of cortical development.