We have grown Au seeded InAs nanowires using chemical beam epitaxy and report on the growth rate dependence on nanowire diameter. We find a maximum of the growth rate at a nanowire diameter of 25 nm, below which the growth rate decreases due to the Gibbs-Thomson effect. Above the maximum, the growth rate decreases with increasing diameter due to the effect of material diffusion to the growth point. A unified model, which accounts for both the Gibbs-Thomson effect and material diffusion, is presented and successfully compared to the experiments. From the comparison, we extract the diffusion length on the substrate surface and a critical diameter, below which nanowire growth ceases, and show that these physical parameters can be tuned by controlling the supersaturation.