  We investigate the production of a quark-antiquark pair in diffractive
photon- proton scattering, approximating soft pomeron exchange by the exchange
of two nonperturbative gluons. In deep inelastic scattering at HERA, events
with two jets and the scattered proton in the final state are predicted to be
observa- ble, with an important contribution from charm production. For
photoproduction of light quark jets with high transverse momentum we find that
both exchanged gluons must have a large invariant mass, so that the cross
section is very small, whereas for charm quarks it is quite appreciable. From
our calculation we also extract the quark structure function of the pomeron for
the scaling variable $z$ no too close to 0 or 1, finding a strong flavour
dependence and a behaviour somewhat harder than $z (1-z)$ for light quarks.
