arXiv:2610.07824v1 Announce Type: cross Abstract: Electrophysiological source imaging (ESI) aims to estimate cortical source activity from noninvasive electrophysiological measurements such as electroencephalogram (EEG). However, ESI is fundamentally ill-posed because source activity is substantially higher-dimensional than sensor observations, resulting in non-unique solutions. Recent learning-based approaches address this ambiguity by learning data-driven source priors, yet they often struggle to generalize across subject-specific cortical geometries. To address this, we propose CANDLE, a learning-based ESI model that estimates source activity on subject-specific cortical geometries. CANDLE learns a prior over the null space induced by the source-to-sensor mapping derived from T1-weighted MRI, restricting learning to unobservable source components while preserving geometric constraints. To train CANDLE, we develop a whole-brain simulator spanning over 1,100 subject-specific cortical geometries with source configurations derived from over 26,000 statistical brain maps. Trained exclusively on simulated data, CANDLE outperformed prior ESI methods on simulated source activity estimation and generalized to two empirical tasks: (i) intracranial stimulation localization from simultaneously recorded scalp EEG and (ii) epileptogenic zone estimation from presurgical interictal EEG. Our project page is available at https://candle-esi.pages.dev}{https://candle-esi.pages.dev.