To facilitate more reliable descriptions of transport properties in liquids, molecular dynamics (MD) simulations are performed based on the effective fragment potential (EFP) method derived from first-principles quantum mechanics (in contrast to MD based upon empirically fitted potentials). The EFP method describes molecular interactions in terms of Coulomb, polarization/induction, dispersion, exchange-repulsion, and charge-transfer interactions. The EFP MD simulations described in this paper, performed on hexane and acetone, are able to track the mean-square displacement of molecules for sufficient time to reliably extract translational diffusion coefficients. The results reported here are in reasonable agreement with experiment.