Lipids in membrane bilayer do exhibit few types of motion, e.g: rotational motion, translation motion, vibration and so on. But I am quite unsure how the motion would like to be for axial diffusion.
Axial diffusion is diffusion of lipid molecules within the same side of bilayer membrane. This kind of diffusion of lipids is very common and its rate is really high. There is another kind of diffusion of lipid molecules called "Lateral Diffusion" in which lipid molecules of the bilayer membrane of one side diffuses to the other side of lipid bilayer although this diffusion rate is quite slow
Thanks for your answer Eugene & Nishant. By the way Nishant, I understand lateral diffusion is motion of the lipid along the parallel direction of the surface. So do you mean the axial diffusion is movement of the lipid from one leaflet to another? I could not get clear picture yet.