In this work a physically sound approach for calculation of the self-diffusion coefficient of model and real fluids is presented. After carrying out a systematic study focused on the equations and molecular dynamic data available in the literature concerning the self-diffusivities of the hard-sphere (HS), square-well (SW) and Lennard-Jones (LJ) fluids, new models are proposed to represent this transport property. First of all, a free-volume-based equation with only one parameter is used to reproduce the recently published data for the HS fluid. Then it is demonstrated that reasonable models for the SW and LJ systems are liable to arise from the HS model by just introducing an attractive contribution. Finally, ii is shown that it is possible to describe the self-diffusivities of real substances in terms of the equations devised for the SW and LJ fluids, which give rise to two-parameter models. These parameters are the diameter and the energy of the considered potential function. Reliable representation is accomplished with the proposed LJ model, the results (AAD = 5.45%) being well comprised by the experimental accuracy. The validation involved the largest database ever used (2514 data points).