Why do water molecules diffuse along axons direction?
The movement is just the thermal energy motion you describe, not due to any concentration difference.
The anisotropy is due to the geometry. White matter tracts are effectively a dense bundle of thick, fatty hoses. Water can freely move in the tubes but cannot move as freely through the dense walls, so you see more movement along the axon length rather than perpendicular to them.
You can read more at https://en.wikipedia.org/wiki/Diffusion_MRI