The self-diffusion of potassium on potassium layers supported by a Ni(001) substrate was studied using quasielastic helium atom scattering. From the broadening of the quasielastic peak in the energy transfer spectra as a function of surface temperature the activation energy for surface diffusion was determined to be 63 +/- 15 meV. This value is of the same order as that found in. the diffusion study of Na on Cu(001) using the same technique. The way in which the energy broadening depends on the transfer of parallel momentum suggests a jump diffusion mechanism.