High-Resolution Dynamic Functional Connectivity Generation with Graph-Variate Flow Matching

Om Roy, Yashar Moshfeghi, Keith Malcolm Smith

High-resolution dynamic functional connectivity (DFC) can reveal rapidly evolving brain-network interactions, but short temporal windows yield noisy, often low-rank covariance estimates. Graph-Variate Dynamic (GVD) connectivity addresses this by modulating fast instantaneous interactions with stable trial-level support. This suppresses spurious fluctuations and emphasizes persistent, informative connections. We show that the Hadamard construction lifts low-rank instantaneous connectivity from the positive-semidefinite to the positive-definite cone, keeping high-resolution trajectories on the SPD manifold without ridge regularisation or post-hoc projection. We introduce GVD-CFM, a class-conditional generative model for high-resolution dynamic connectivity. Each trial is represented as SPD GVD matrices on a product Riemannian manifold, then mapped through a global log-Euclidean diffeomorphism and an invertible temporal DCT basis. A Transformer-based conditional flow models all spectral modes jointly and generates the full trajectory non-autoregressively in Euclidean coordinates while preserving exact correspondence with valid SPD sequences. Retaining the full DCT basis also enables…