We characterize the atomic mobility behavior driven by vacancies, in bcc and fcc Fe-Cr diluted alloys, using a multi-frequency model. We calculate the full set of the Onsager coefficients and the tracer self and solute diffusion coefficients in terms of the mean jump frequencies. The involved jump frequencies are calculated using a classical molecular static (CMS) technique. For the bcc case, we also perform quantum calculations based on the density functional theory (DFT). There, we show that, in accordance with Bohr's correspondence principle, as the size of the atomic cell (total number of atoms) is increased, quantum results with DFT recover the classical ones obtained with CMS calculations. This last ones, are in perfect agreement with available experimental data for both, solute and solvent diffusion coefficients. For high temperatures, in the fcc phase where no experimental data are yet available, our CMS calculations predict the expected solute and solvent diffusion coefficients.