The Stokes–Einstein (SE) equation is often applied as an approximation of self-diffusion coefficients D of molecular species based on the shear viscosity of fluids. The SE relation gives rough estimates of self-diffusion coefficients in liquid states and (divergently) high deviations for the gaseous phase. Inspired by Rosenfeld’s entropy scaling approach, we find a universal function of residual entropy f(s res) to describe the ratio between experimental and calculated D from SE equation for all investigated substances. The so-obtained modified SE equation, containing 5 universal parameters adjusted to experimental data of 61 substances of 11 different chemical families, can be used for predicting D in the entire fluid region, with averaged absolute deviations of 12.3% compared to experimental data (5407 data points). The application of the proposed model to diffusion coefficients at infinite dilution shows average deviations of 20.8% for widely different systems (412 data points).