Massless quark and antiquark jet production at large transverse momentum in the coherent diffractive processes at hadron colliders is calculated in the two-gluon exchange parametrization of the Pomeron model. We use the helicity amplitude method to calculate the cross section formula. We find that for the light quark jet production the diffractive process is related to the differential off-diagonal gluon distribution function in the proton. We estimate the production rate for this process at the Fermilab Tevatron by approximating the off-diagonal gluon distribution function by the usual diagonal gluon distribution in the proton. And we find that the cross sections for the diffractive light quark jet production and the charm quark jet production are in the same order of magnitude. We also use the helicity amplitude method to calculate the diffractive charm jet production at hadron colliders, by which we reproduce the leading logarithmic approximation result of this process we previously calculated.