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

High-resolution dynamic functional connectivity (DFC) is attractive for studying rapidly evolving brain-network interactions, but it is difficult to estimate and generate reliably because short temporal windows produce noisy and often low-rank covariance estimates. Graph-Variate Dynamic (GVD) connectivity addresses this problem by modulating fast instantaneous interactions with a stable trial-level support, suppressing spurious fluctuations while emphasizing persistent and informative connections. We further show that this Hadamard construction lifts low-rank instantaneous connectivity from the positive-semidefinite to the positive-definite cone, enabling high-resolution connectivity trajectories to remain on the SPD manifold without additive ridge regularisation or post-hoc projection. Building on this structure, we introduce GVD-CFM, a class-conditional generative model designed specifically for high-resolution dynamic connectivity generation. Each trial is represented as a sequence of SPD GVD matrices on a product Riemannian manifold and mapped through a global log-Euclidean diffeomorphism and an invertible temporal DCT basis. A Transformer-based conditional flow models all spectral modes jointly, allowing the complete high-resolution trajectory to be generated non-autoregressively in Euclidean coordinates while preserving exact correspondence with valid SPD connectivity sequences. Because the full DCT basis is retained, the learned representation also defines a temporal basis expansion that can be decoded on denser temporal grids without retraining.Across multiple EEG motor-imagery datasets, GVD-CFM achieves the strongest overall performance across held-out distributional fidelity, preservation of temporal dynamics, and synthetic-to-real classification, while remaining computationally efficient relative to strong raw-signal and direct GVD-space generative baselines. These results establish GVD-CFM as a framework for generating realistic, temporally coherent, high-resolution brain-network trajectories while preserving manifold structure and supporting resolution-flexible decoding from a single trained model.