We present two related probabilistic methods for neural source reconstruction from MEG/EEG data that reduce effects of interference, noise, and correlated sources. Both methods localize source activity using a linear mixture of temporal basis functions (TBFs) learned from the data. In contrast to existing methods that use predetermined TBFs, we compute TBFs from data using a graphical factor analysis based model [Nagarajan, S.S., Attias, H.T., Hild, K.E., Sekihara, K., 2007a. A probabilistic algorithm for robust interference suppression in bioelectromagnetic sensor data. Stat Med 26, 3886–3910], which separates evoked or event-related source activity from ongoing spontaneous background brain activity. Both algorithms compute an optimal weighting of these TBFs at each voxel to provide a spatiotemporal map of activity across the brain and a source image map from the likelihood of a dipole source at each voxel. We explicitly model, with two different robust parameterizations, the contribution from signals outside a voxel of interest. The two models differ in a trade-off of computational speed versus accuracy of learning the unknown interference contributions. Performance in simulations and real data, both with large noise and interference and/or correlated sources, demonstrates significant improvement over existing source localization methods.