The wide scatter in experimental results has not allowed drawing solid conclusions on self-diffusion in the chalcopyrite CuInSe2 (CIS). In this work, the defect-assisted mass transport mechanisms operating in CIS are clarified using first-principles calculations. We present how the stoichiometry of the material and temperature affect the dominant diffusion mechanisms. The most mobile species in CIS is shown to be copper, whose migration proceeds either via copper vacancies or interstitials. Both of these mass-mediating agents exist in the material abundantly and face rather low migration barriers (1.09 and 0.20 eV, respectively). Depending on chemical conditions, selenium mass transport relies either solely on selenium dumbbells, which diffuse with a barrier of 0.24 eV, or also on selenium vacancies whose diffusion is hindered by a migration barrier of 2.19 eV. Surprisingly, indium plays no role in long-range mass transport in CIS; instead, indium vacancies and interstitials participate in mechanisms that promote the formation of antisites on the cation sublattice. Our results help to understand how compositional inhomogeneities arise in CIS.