Molecules in fluids diffuse because they are in constant, random motion in which molecules are more likely to move to where there are fewer of the same types of molecules. Therefore, diffusion really occurs as a matter of probability combined with the random motion of molecules, which is actually heat energy. The hotter a fluid is, the more rapidly substances diffuse in it.
Diffusion occurs because of Brownian motion, which is the constant, random movements of particles in fluids. Each atom or molecule in a fluid, whether solute or solvent, is constantly moving in a straight line, at a rate determined by temperature, according to the HyperPhysics project at Georgia State University. When the particle encounters another particle or a solid surface, it bounces off in a different direction. If it is another particle in the fluid, the paths of both particles are altered.
This is why a water-soluble dye, when dropped in water, eventually spreads through the water even without stirring. Even in still water, individual water molecules are constantly moving. When they strike the molecules of the dye, they impart motion to them. At least some of the time, that motion takes them away from other dye molecules, spreading the dye. If there is more water than dye, the motion of the dye molecule is more likely to be away from other dye molecules than toward them.