Recently, an alternative approach to self-diffusion in atomic liquids was proposed by one of us [Vergeles, hi., Szamel, G. Chem. Phys. 1999, 110, 3009]. This approach is applicable where the concept of binary collisions breaks down and the self-diffusion coefficient is small. Predictions from this method are in quantitative agreement with molecular dynamics (MD) simulations, over a broad range of densities and temperatures, for an atomic liquid interacting with a repulsive r(-12) potential. Here we extend this approach to include attractive interactions; we study a liquid interacting with the Lennard-Jones (LJ) potential. Theoretical predictions are compared to MD simulations results. To clarify the role of attractive interactions, we compare LJ results with those obtained with the repulsive part of the LJ potential. Conclusions about the role of the attractive forces in self-diffusion are discussed.