Objective: To infer information flow in the white matter of the brain and recover cortical activity using functional MRI, diffusion MRI, and MEG without a manual selection of the white matter connections of interest. Approach: A Bayesian network which encodes the priors knowledge of possible brain states is built from imaging data. Diffusion MRI is used to enumerate all possible connections between cortical regions. Functional MRI is used to prune connections without manual intervention and increase the likelihood of specific regions being active. MEG data is used as evidence into this network to obtain a posterior distribution on cortical regions and connections. Main results: We show that our proposed method is able to identify connections associated with the a sensory-motor task. This allows us to build the Bayesian network with no manual selection of connections of interest. Using sensory-motor MEG evoked response as evidence into this network, our method identified areas known to be involved in a visuomo-tor task. In addition, information flow along white matter fiber bundles connecting those regions was also recovered. Significance: Current methods to estimate white matter information flow are extremely invasive, therefore limiting our understanding of the interaction between cortical regions. The proposed method makes use of functional MRI, diffusion MRI, and M/EEG to infer communication between cortical regions, therefore opening the door to the non-invasive exploration of information flow in the white matter.