Extrinsic diffusion of zinc (Zn) in gallium antimonide (GaSb) under Ga-rich conditions was analyzed on the basis of the kick-out and the dissociative diffusion mechanism. Accurate modeling of the experimental profiles by means of continuum theoretical calculations reveals that Zn diffusion proceeds via singly positively charged Zn interstitials $({\mathrm{Zn}}_{i}^{+})$. The changeover of ${\mathrm{Zn}}_{i}^{+}$ to substitutional gallium (Ga) sites, thereby forming the acceptor dopant ${\mathrm{Zn}}_{\mathrm{Ga}}^{\ensuremath{-}}$, is concluded to be mainly mediated by neutral ${I}_{\mathrm{Ga}}^{0}$ and singly positively charged Ga interstitials ${I}_{\mathrm{Ga}}^{+}$ via the kick-out mechanism. Fitting of the Zn profiles provides the reduced ${\mathrm{Zn}}_{i}^{+}$-mediated Zn diffusion coefficient and the relative contributions of ${I}_{\mathrm{Ga}}^{0}$ and ${I}_{\mathrm{Ga}}^{+}$ to Ga diffusion. These contributions to Ga diffusion are lower than the directly measured Ga diffusion coefficient, which indicates that Ga diffusion in GaSb is rather mediated by Ga vacancies than by Ga interstitials even under Ga-rich conditions. This finding supports the transformation reaction between native point defects in GaSb that was previously proposed to explain the Ga-vacancy-mediated diffusion of Ga in GaSb under Ga-rich conditions [H. Bracht et al. Nature (London) 408, 69 (2000)].