A microscopic approach has been developed for the self as well as cross diffusivity:of a binary fluid mixture based on the concepts of mode coupling theory. Illustrative numerical results-calculated for a Lennard-Jones fluid mixture are presented and are shown to be in good agreement with the available computer simulation;results. The effects of mass, composition, interaction strength, and sizes of the components on the diffusivities are studied in order to obtain insight into the role of different modes in the diffusion process;:The mass dependence of diffusivity is found to be weak with a power law behavior in contrast to the:Enskog theory prediction of strong mass dependence. Also the mass and concentration of one component are found to have significant and interesting effects on the diffusivity of the other component. The new expressions derived here are shown to predict positive values for the cross diffusion constant over the various parameter ranges considered, which is consistent with the simulation results but unpredicted by other commonly used models. It is also found that the cross diffusion is significant in liquid Lorentz-Berthelot mixture-for size ratio unity, strong interaction potential, and intermediate composition range.