We present results on diffractive production of hard processes in
pbar p collisions at sqrt s = 1.8 TeV at the Tevatron using the CDF detector.
The signatures used to identify diffractive events are the forward rapidity
gap and/or the detection of a recoil antiproton with high forward momentum.
We have observed diffractive W-boson, dijet, and heavy quark production.  We
also present results on double-pomeron production of dijets.