We expose the predominant diffusional pathways for In and As in InAs, as well as dopant Si atoms in InAs, using Nudged Elastic Band calculations in conjunction with accurate Density Functional Theory calculations of the energy of defective systems. Our results show that As is a very fast diffuser compared to In and Si for both vacancy-assisted and interstitially mediated mechanisms. Larger indium atoms, on the other hand, are very slow diffusers and strongly prefer to remain on the In sublattice. Silicon also prefers to stay in substitutional sites in the In sublattice, in agreement with the fact that Si is used to create n-doped InAs. We find that the mechanism by which Si diffuses within the InAs lattice is very unlikely to proceed via vacancy-assisted jumps, since these routes encounter energy barriers above 2 eV. In contrast, silicon can readily make interstitial jumps since they occur with energy barriers as small as 0.23 eV. This suggests that an interstitial diffusion mechanism is strongly preferred for Si diffusion in InAs which challenges the common presumption made for another similar III-V compound, namely GaAs, that Si diffusion takes place via a vacancy-assisted mechanism.