Hadronic diffractive processes characterized by a hard scale (hard diffraction) contain a nontrivial interplay of hard and soft, nonperturbative interactions, which breaks down factorization of short and long distances. On the contrary to the expectations based on the factorization hypothesis, assuming that hard diffraction is a higher twist, these processes should be classified as a leading twist. We overview various implications of this important observation for diffractive radiation of Abelian (Drell-Yan, gauge bosons, Higgs boson) and non-Abelian (heavy flavors) particles, as well as direct coalescence into the Higgs boson of the nonperturbative intrinsic heavy flavor component of the hadronic wave function.