Diffusion is a physical process where molecules of a material move from an area of high concentration (where there are many molecules) to an area of low concentration (where there are fewer molecules)
Diffusion usually happens in a solution in gas or in a liquid. But diffusion is not confined to gases and liquids only. It can take place with matter in any state. For example, salt diffuses (dissolves) into water; a sugar cube is left in a beaker of water for a while diffuses (dissolves) into water ; water diffuses (evaporates) into the air. It is even possible for a solid to diffuse into another solid; e.g., pure gold will diffuse into pure lead, two pieces of chalk tightly wrapped together are found to become homogeneous after some years; although at room temperature this diffusion is very slow. Generally, gases diffuse much faster than liquids, and liquids much faster than solids. So Yes solid diffuse !