In the Stranski-Krastanow growth of strained pseudomorphic films, material transport by surface diffusion plays a crucial role for the development of the three-dimensional island morphology. In an attempt to elucidate the atomistic aspects of this growth mode, we study diffusion of a single indium adatom on (1ϫ3)-and (2 ϫ3)-reconstructed subcritical In 2/3 Ga 1/3 As(001) films using first-principles total energy calculations of the corresponding adiabatic potential-energy surfaces ͑PES͒. We find that In diffusion is anisotropic, and substantially enhanced compared to the conventional GaAs͑001͒-c(4ϫ4) substrate. Special attention is also paid to the methodology of deriving the tracer diffusion coefficients of indium from knowledge of the PES, using the continuous-time random-walk formalism.