Does diffusion MRI measure diffusion or osmosis? I am trying to understand the physical property which is measured in diffusion weighted imaging (DWI) and diffusion tensor imaging (DTI). I read that these methods estimate the apparent diffusion coefficient (in DWI) or the diffusion tensor (in DTI). 
My understanding is that diffusion usually refers to the net movement of a solute (e.g. salt) dissolved in a solvent (e.g. water) from a region of higher concentration to lower concentration. 
My understanding is that osmosis usually refers to the net movement of water across a semi-permeable membrane from a region of low solute concentration to region of higher solute concentration. 
I read that DWI and DTI measure the "diffusion of water". For example, in the white matter tracts of the brain, "water diffuses at a higher rate along the tract direction than perpendicular to the tract direction". What physical process is this referring to? Is this referring to a net flow of water along the white matter tracts (osmosis?), or the rate at which some solute dissolved in this water could diffuse?
I am struggling to phrase this question clearly, but the main thing I am trying to understand is the physical significance of the quantities measured by DWI and DTI -- the phrase "diffusion of water" does not mean much to me.
 A: Diffusion is basically driven by molecular motion, eg Brownian motion. 
Diffusion measures how a certain marked molecule spreads in the surrounding due to molecular motion. Usually, people think of some kind of marker molecule, eg ink in water. If you would like to measure the Brownian motion of water itself, you would also do a diffusion experiment and find yourself with the problem that the diffusion is different for each marker molecule, so you would try to use the least possible amount of the marker to approximate a situation where no marker molecule is present, so its diffusion approximates the Brownian motion of the water.
Imagine now you could color the water molecules themselves. This can be done by NMR: You excite them and apply a position-dependent phase to their magnetic moments. After a while, you reverse the effect. If no Brownian motion is present, you would end up with the same signal as before the position-dependent phase. If motion is present, however, you measure a reduced signal and from this you can deduce the Brownian motion, which basically is the diffusion of water molecules in water.
The water is the medium and the marker molecule at the same time. 
