BOLDFlow: Network-Level Recovery of fMRI Connectivity from EEG via Conditional Flow Matching

Functional connectivity (FC) analyses operate on correlations between regional blood-oxygen-level-dependent (BOLD) signals, but estimating them requires functional magnetic resonance imaging (fMRI). Inferring fMRI-like connectivity from scalp electroencephalography (EEG) could broaden access, yet per-region regressors and joint mean-squared-error decoders collapse toward the conditional mean, discarding the residual cross-region covariance. We present BOLDFlow, which models the conditional distribution of parcellated BOLD activity using conditional flow matching with a learned EEG-conditioned source. Sampled trajectories retain the model's residual cross-region covariance, while repeated draws provide input-conditional ensemble spread without a separate uncertainty head. In subject-disjoint evaluations on two simultaneous in-scanner EEG–fMRI datasets spanning rest and sleep, BOLDFlow improves measured-FC recovery (NeuroBOLT: $0.428$ to $0.584$; OpenNeuroSleep: $0.340$ to $0.528$) and temporal correlation ($0.272$ to $0.326$ and $0.151$ to $0.212$, respectively), and scales to output parcellations with 512 components. The recovered connectomes retain individual-specific and community structure, while ensemble spread attains nominal coverage after single-parameter recalibration.