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In liquids the molecules are loosely packed than solids that means the movement of particles is much higher as compared to solids. So they tend to move freely. Diffusion is a process in which particles(molecules,etc.) move from higher concentration to lower concentration. This is only possible if the molecules are loosely packed(i.e.,intermolecular forces is minimum and space is maximum). In solids this phenomena is not possible because the constituent particles are tightly packed and are not free to move about hence diffusion in solids does not occur.
The inter molecular forces between the particles in liquids is very less compared to that of solids.the inter molecular spaces in liquids is more than solids.that means they are loosely packed which helps them in moving easily.diffusion is the process of movement of substances from higher conc. to lower conc.