First of all, decoherence is not an interpretation, but an experimental fact. Theoretically, it is a direct consequence of the Schrodinger equation applied to a large number of degrees of freedom.
Decoherence is a deterministic process, in which probability evolves deterministically. In this process quantum probabilistic laws effectively evolve towards classical ones, thus explaining why, on the macroscopic level, for all practical purposes we can use classical statistical mechanics. More precisely, decoherence provides a continuous deterministic mechanism by which the interference terms in the probability density become dynamically suppressed.
Decoherence also plays an important role in some interpretations of QM, especially many-world and Bohmian. But these interpretations (controversial just as all other interpretations) should be distinguished from decoherence itself which is not controversial at all.
