We report new results from CDF on single-diffractive dijet and W/Z production, and on exclusive dijet, diphoton, and dilepton production in proton-antiproton collisions at s**(1/2) = 1.96 TeV at the Fermilab Tevatron. The measured exclusive dijet and diphoton cross sections provide a test of theoretical predictions for exclusive Higgs production at the LHC.