Diffractive parton distribution functions give the probability to find a parton in a hadron if the hadron is diffractively scattered. We provide an operator definition of these functions and discuss their relation to diffractive deeply inelastic scattering and to photoproduction of jets at HERA. We perform a calculation in the style of ``constituent counting rules'' for the behavior of these functions when the detected parton carries almost all of the longitudinal momentum transferred from the scattered hadron.

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