The pressure dependence of the self-diffusion in simple nonpolar liquids has been examined. It is shown that an equation based on Lamm's formalism provides an adequate representation of the variation of self-diffusion with pressure at constant temperature over wide ranges of pressure and temperature. Data on cyclohexane, n-hexane, benzene, tetramethylsilane, methylcyclohexane, and chlorotrifluoromethane conform to this behavior. The analysis presented herein provides a method for estimating self-diffusion coefficients at elevated pressure from a knowledge of the shear viscosity coefficient values under the same conditions without introducing any adjustable parameters.