  We consider the diffractive Drell-Yan process in proton-(anti)proton
collisions at high energies in the color dipole approach. The calculations are
performed at forward rapidities of the leptonic pair. Effect of eikonalization
of the universal "bare"dipole-target elastic amplitude in the saturation regime
takes into account the principal part of the gap survival probability. We
present predictions for the total and differential cross sections of the single
diffractive lepton pair production at RHIC and LHC energies. We analyze
implications of the QCD factorisation breakdown in the diffractive Drell-Yan
process, which is caused by a specific interplay of the soft and hard
interactions, and resulting in rather unusual properties of the corresponding
observables.
