A methodology for computing Fick diffusivities directly from equilibrium molecular dynamics (MD) simulations is presented and validated for acetone-methanol and acetone-tetrachloromethane liquid mixtures. Fick diffusivities are obtained from Maxwell-Stefan (MS) diffusivities and the so-called thermodynamic factor. MS diffusivities describe the friction between different components, while the thermodynamic factor is the concentration derivative of the activity describing the deviation from ideal mixing behavior. It is important to note that all mutual diffusion experiments measure Fick diffusion coefficients, while molecular simulation provides MS diffusivities. The required thermodynamic factor to convert MS into Fick diffusivities and vice versa, however, is usually difficult to extract from both simulations and experiments leaving a gap between theory and application. Here, we employ our novel method to compute the thermodynamic factor from small-scale density fluctuations in equilibrium MD simulations [Chem. Phys. Lett.2011, 504, 199-201]. Previously, this method was developed and validated for molecules with single interaction sites only. In this work, we applied this method to acetone-methanol and acetone-tetrachloromethane liquid mixtures and show that the method also works well in these more complex systems. This provides the missing step to extract Fick diffusion coefficients directly from equilibrium MD simulations. The computed Fick diffusivities of acetone-methanol and acetone-tetrachloromethane mixtures are in excellent agreement with experimental values. The suggested framework thus provides an efficient route to model diffusion in liquids on the basis of a consistent molecular picture.