  We consider photon-initiated events with large rapidity gaps in proton-proton
collisions, where one or both protons may break up. We formulate a modified
photon PDF that accounts for the specific experimental rapidity gap veto, and
demonstrate how the soft survival probability for these gaps may be implemented
consistently. Finally, we present some phenomenological results for the
two-photon induced production of lepton and $W$ boson pairs.
