Dear Xiong,
my understanding is that the definition of the diffusion coefficient is simmilar to the one of the attenuation coefficient - meaning that when a photon beam passes 1 meter of material with a diff. coeff of 1 m^-1, only 1/e of initial photons would pass without being diffused.
However, I am not 100% sure with this - I will ask another expert for confirmation.
Vojtěch