The effects of high pressure and free volume on the mutual-, tracer-, and self-diffusion coefficients of pure components and binary mixtures of light gases and hydrocarbons (both pure and mixed) are addressed from the continuum mechanical and classical thermodynamics standpoint. First, an analogy between the friction between two macroscopic bodies and the friction at microscopic level is proposed so that the pressure is incorporated into constitutive equations for diffusion from the continuum mechanical theory. Then, by making use of the local equilibrium assumption, the fugacity coefficient and the compressibility factor, defined at equilibrium, are introduced into such modified constitutive equations. The suggested method allows us to derive some expressions for diffusion coefficients found in the open literature. Besides, it was found that the calculated diffusion coefficients are in agreement with experiments for free volume fractions larger than 0.2 approximately. Hence, a wider range was obtained by incorporating not only the pressure but also the free volume fraction into the constitutive equations. The final expressions for estimating the diffusion coefficients are in better agreement with experiments than some correlations from the open literature for the entire range of free volume fractions, which are estimated by using parameters from the PC-SAFT and the PR equations of state.