On the basis of the free volume theory and activation energy concept, a fundamental equation which takes into account the effects of temperature and pressure has been developed. By introducing different expressions for the free volume and activation energy, several equations for fluid diffusion coefficients were derived accordingly. With the van der Waals free volume and internal energy formula, a three-parameter model for fluid diffusion coefficients at moderate pressure was obtained. The grand average absolute deviation percent of 345 data points (44 systems) for self- and infinite dilute inter-diffusivities is 2.32, against the results of the model of Cohen and Turnbull, 4.13. In particular, by means of the modified Carnahan n-Starling free volume equation, a four-parameter model with average abosolute deviation percent 2.64 (30 systems, 644 data points) for the estimation of dense fluid inter- and self-diffusivities at high pressures and in supercritical conditions was derived. The derived model is superior to the method of Lee and Thodos for most substances, especially for strongly polar ones.