We present real-time X-ray scattering studies of the influence of silicon on the homoepitaxial growth mode of GaN grown by metal-organic vapor-phase epitaxy. Both annealing of Si-doped GaN and surface dosing of GaN with disilane are shown to change the mode of subsequent growth from step-flow to layer-by-layer. By comparing the growth behavior induced by doped layers which have been annealed to that induced by surface dosing, we extract an approximate diffusion coefficient for Si in GaN of 3.5 x 10(-18) cm(2)/s at 810 degreesC.