Diffusion in the unannealed material faster due to the presence of nonequilibrium defects and stress. Both quickly disappears when the temperature rises above about 0.8 Tm
Annealing is a heat treatment process usually at an elevated temperature and it is used to remove stress and defects after growth/deposition processes. It is also sometimes performed to alter the mechanical and electrical properties of materials and it is accompanied by diffusion. Diffusion or solid state diffusion on the other hand is a material transport process as a result of differences in concentration gradient and is temperature dependent through the Arrhenius equation. Annealing process leads to densification as a result of atomic migration (Diffusion) to removed voids.