The roughness relaxation of thin columnar Au electrodeposits at constant potential and 25°C in 0.05 M NaF, 0.05 M KCl and 0.05 M K2SO4 has been studied. These measurements were taken in the −0.6 to 0.8 V (vs Hg/Hg2SO4 reference electrode) potential range. The kinetic data were obtained from the roughness factor decay over 5 × 104 s. The value of the surface diffusion coefficient Ds of Au atoms was derived from the roughness decay law at constant potential and pH. At any potential, the value of Ds increases in the order NaF < K2SO4 < KCl. This sequence correlates with the specific adsorption of anions on Au. In K2SO4 and NaF solutions, as the electroformation of AuOH species takes place, the effect of SO42− and F− ions is no longer observed. In contrast, in 0.05 M KCl solution, the value of Ds increases steadily as the applied potential is increased positively.