The diffusion rate varies inversely with distance , and directly with temperature , concentration gradient , area through which diffusion takes place, and a fudge factor called the diffusion coefficient . The diffusion coefficient is empirically determined and varies with molecular size along with other attributes and solvent characteristics. Membrane flux is diffusion across a membrane. A membrane can act as a barrier or enhancer to diffusion. Certainly diffusion across a membrane will be different from that in the solvent.
Osmosis is always and only the diffusion of water through a selectively permeable membrane .
So, there must always be water present and a membrane that allows some water through it, but some of the solutes in the water permeate the membrane at a different rate than water creating a concentration difference on the two sides of the membrane. Remember that all chemicals in solution prefer to be equally distributed if all other things are equal. If water penetrates a membrane faster than one of its solutes, then the water concentration is out of balance. The water concentration is a reciprocal of the concentration of all of the solutes. One can express the osmotic pressure of a solution with a formula assuming that no solute can penetrate the membrane.