The possible smoothing effect that diffusion has on steep plasmapause density gradients is examined for diffusion estimated from (a) the Bohm diffusion coefficient and (b) scattering by observed electrostatic waves. For characteristic plasma temperatures and magnetic fields at an L=4 plasmapause, the (equatorial) perpendicular Bohm diffusion coefficient is approximately DB =0.12¿10-4 RE2 /h. The estimate for diffusion resulting from scattering by observed electrostatic waves is much lower: D⊥,E =0.27¿10-7 RE2 /h. However, this diffusion rate may be too small an estimate if, as is probable, the wave amplitudes are significantly higher for steep plasmapauses. Thus the effects are negligible for most considerations of macroscopic plasmapause dynamics but could be significant in limiting drift wave instabilities and similar phenomena which are driven by the steepness of the plasmapause density gradient. If Bohm diffusion is operative, the minimum persistent plasmapause scale length should be of the order 10-2 RE, or ~60 km.