Alzheimer's Disease Classification via Score-Derived Spectral Coupling from Longitudinal Cortical Data

Longitudinal neuroimaging provides direct observations of within-subject disease-related change, but such data are typically sparse and irregularly sampled. We propose a spherical score-based framework for learning class-conditioned coupling representations from pairwise longitudinal cortical observations drawn from trajectories with two or more timepoints. Given a baseline-follow-up pair, we represent the interval-normalized cortical change in the spherical harmonic (SH) domain and train a class-conditioned score model using a spherical Ornstein-Uhlenbeck diffusion process. Rather than using the learned score for generation, we exploit its local differential structure: the negative score Jacobian defines a state-dependent local dependency operator over SH modes, reducing to the precision matrix in the Gaussian special case. We convert this score-derived operator into a normalized guidance operator and use it to modulate intermediate spectral features of a spherical cortical network under alternative diagnostic hypotheses. The proposed framework is evaluated on longitudinal cortical thickness, FDG-PET, and AV45-PET data from the ADNI dataset, achieving consistently strong classification performance across modalities. Additional cross-cohort and dataset-shift evaluations further support the generalizability of the learned coupling representation.