Diffusion in a series of ionic liquids is investigated by a combination of Broadband Dielectric Spectroscopy (BDS) and Pulsed Field Gradient Nuclear Magnetic Resonance (PFG NMR). It is demonstrated that the mean jump lengths increase with the molecular volumes determined from quantum-chemical calculations. This provides a direct means-via Einstein-Smoluchowski relation-to determine the diffusion coefficient by BDS over more than 8 decades unambiguously and in quantitative agreement with PFG NMR measurements. New possibilities in the study of charge transport and dynamic glass transition in ionic liquids are thus opened.