We present the results of a molecular simulation study of fluid mixtures, where complex diffusion behavior has experimentally been found and offer an explanation based on the hydrodynamic and thermodynamic components of the Fick diffusion coefficient. Special attention is paid to mixtures near critical and demixing regions, where in many cases strong discrepancies between different measurements of the Fick diffusion coefficients are found. Also molecular simulations are challenging in these regions and require extensive sampling due the presence of pronounced density fluctuations.