Apparently this is a term denoting rotational diffusion of the lipid molecule about its axis

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.

Eugene is correct. Movement from one leaflet to another is usually known as the flip-flop rate.

http://www.sciencedirect.com/science/article/pii/S0006349508704648

Dear Jeffrey, thanks so much for the link.