Exclusive Higgs production, in which the event consists of nothing but the leading protons and a Higgs boson, has been proposed as a channel in which to study the properties of the Higgs boson at the Large Hadron Collider (LHC). Although we do not expect to observe exclusive Higgs-boson production at the Tevatron, we can observe similar processes which provide a calibration for theoretical predictions of exclusive Higgs production at the LHC. The CDF measurements of exclusive dijet and diphoton production, examples of such processes, are presented in Sec. 2. Single diffraction has been studied extensively at the Tevatron in Run I, including diffractive dijet and W/Z-boson production. New results with extended kinematical reach allowed by the larger Run II dataset are presented in Sec. 3. CDF II includes forward detectors designed for studying diffractive physics. The MiniPlug calorimeters cover the pseudorapidity region 3.5<|{eta}|<5.1. Beam Shower Counters (BSC) surrounding the beampipe in several locations detect particles in the forward region 5.4<|{eta}|<7.4. A spectrometer consisting of three Roman-pot detectors preceded by Tevatron dipoles is used to track diffractive antiprotons which have lost a fraction 0.03<{zeta}<0.10 of the beam momentum
