We present here a microscopic and self-consistent calculation of the self-diffusion coefficient of a small tagged particle in a dense liquid of much larger particles. In this calculation the solute motion is coupled to both the collective density fluctuation and the transverse current mode of the liquid. The theoretical results are found to be in good agreement with the known computer simulation studies for a wide range of solute-solvent size ratio. In addition, the theory can explain the anomalous enhancement of the self-diffusion over the Stokes-Einstein value for small solutes, for the first time. Further, we find that for large solutes the crossover to Stokes-Einstein behavior occurs only when the solute is 2-3 times bigger than the solvent molecules. The applicability of the present approach to the study of self-diffusion in supercooled liquids is discussed.