We characterize a class of environmental noises that decrease the coherent properties of quantum channels by introducing and analyzing the properties of dephasing superchannels. These are defined as superchannels that affect only nonclassical properties of a quantum channel E , i.e., they leave invariant the transition probabilities induced by E in the distinguished basis. We prove that such superchannels ΞC form a particular subclass of Schur-product supermaps that act on the Jamiołkowski state J (E ) of a channel E via a Schur product, J'=J ∘C . We also find physical realizations of general ΞC through pre- and postprocessing employing dephasing channels with memory, and we show that memory plays a nontrivial role for quantum systems of dimension d >2 . Moreover, we prove that the coherence-generating power of a general quantum channel is a monotone under dephasing superchannels. Finally, we analyze the effect that dephasing noise can have on a quantum channel E by investigating the number of distinguishable channels that E can be mapped to by a family of dephasing superchannels. More precisely, we upper-bound this number in terms of hypothesis-testing channel divergence between E and its fully dephased version, and we also relate it to the robustness of coherence of E .