  We calculate for the first time cross sections for single and central
diffractive as well as exclusive diffractive production of dilepton pairs in
proton-proton collisions. Several differential distributions are shown. The
inclusive diffractive processes are calculated using diffractive parton
distributions extracted from the analysis of diffractive structure function and
dijet production at HERA. We find that the inclusive single-diffractive
Drell-Yan process is by about 2 orders of magnitude smaller than ordinary
Drell-Yan process. The central-diffractive processes are smaller by one order
of magnitude compared to single-diffractive ones. We consider also exclusive
production of dilepton pairs. The exclusive photon-pomeron (pomeron-photon)
process constitutes a background to the QED photon-photon process proposed to
be used for controlling luminosity at LHC. Both processes are compared then in
several differential distributions. We find a region of the phase space where
the photon-pomeron or pomeron-photon contributions can be larger than the
photon-photon one.
