The natural line of the incoherent quasi-elastic neutron scattering law of liquid potassium has been obtained from experimental double-differential scattering cross-sections at the temperatures of 340, 440, and 550 K for wavevector transfers in the range of 0.27 less than or equal to Q less than or equal to 1.13 Angstrom(-1). The full width at half maximum of this line as a function of Q(2) has been analysed on the basis of several diffusion models. It has been found that the self-diffusion process in liquid potassium has an individual and activationless character and can be approximately described by means of the mode-coupling theory at temperatures noticeably more than the melting point.