In this work, the Enskog solution of the Boltzmann equation coup led with the Weeks - Chandler-Andersen perturbation theory of liquids is shown to be an excellent approach for correlating and predicting self-diffusivities of dense fluids. Afterwards, this theory is used to estimate mutual-diffusion coefficients of solutes at infinite dilution in sub- and supercritical solvents. The approach presented here is based on the smooth hard-sphere theory, in which the coupling factor of the rough hard-sphere theory relating translational and rotational motions is made unity, and using the Speedy correlation which has been proposed as a model of self-diffusion coefficient of hard-sphere fluids. The methodology presented here only makes use of pure component information and density of mixtures affording predictions without any binary adjustable parameters. Since the behavior of mutual-diffusion coefficients in the proximity of a binary critical point is of great interest, calculations were also accomplished in the Liquid phase along the gas-liquid boundary when experimental data of both binary vapor-liquid equilibrium and densities of mixture were available.