Spherical Brownian Bridge Diffusion Models for Conditional Cortical Thickness Forecasting

2025-09-10

AI Summary

Accurately predicting individualized, high-resolution cortical thickness (CTh) trajectories faces two key challenges: modeling non-Euclidean cortical geometry and effectively fusing multimodal data. To address these, we propose the Conditional Spherical U-Net (CoS-UNet), the first framework integrating a spherical Brownian bridge diffusion model with a bidirectional conditional generative mechanism to jointly model factual and counterfactual CTh trajectories. CoS-UNet employs spherical convolution and dense cross-attention to jointly encode structural MRI, cognitive scores, and other heterogeneous longitudinal data on the cortical sphere. Evaluated on the ADNI and OASIS longitudinal cohorts, our method significantly reduces vertex-wise CTh prediction error (p < 0.001). It enables submillimeter-accurate, subject-specific dynamic trajectory inference and early detection of neurodegenerative change. The geometrically grounded, interpretable architecture advances brain-age modeling and supports data-driven intervention planning.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Multimodal Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Forecasting individualized cortical thickness trajectories on cerebral cortex
• Integrating multi-modal data for subject-specific non-Euclidean predictions
• Generating factual and counterfactual cortical development scenarios

Innovation

• Spherical Brownian Bridge diffusion process forecasting
• Conditional spherical U-Net with cross-attention integration
• Individualized cortical thickness trajectory generation framework