We propose an alternative approach to self-diffusion in an atomic liquid. Our starting point is an oscillatory motion of a tagged particle in its first solvation shell (cage). Only after cage relaxation is taken into account is the tagged particle able to diffuse. This approach is suitable for describing liquids where the concept of binary collisions breaks down and the self-diffusion coefficient is small. Our predictions quantitatively agree with the results of MD simulations in a broad range of densities and temperatures up to the freezing transition.