Starting from a density-matrix treatment of carrier-phonon interaction based on a recent reformulation of the Markov limit, we provide a detailed investigation of phonon-induced quantum diffusion in semiconductor nanostructures. In particular, as for the case of carrier-carrier relaxation in photoexcited semiconductors, our analysis shows the failure of simplified dephasing models in describing phonon-induced scattering non-locality, pointing out that such limitation is particularly severe for the case of quasielastic dissipation processes.