One may think at first glance, that the diffusivity is a phenomenon limited to the molecular scale. However, diffusivity is also present at the granular level. You may ask, how can granular particles diffuse if there are no stochastic fluctuations at this stage? And even more when one is dealing with granular media at high volume fractions? The resistance to accept this is reasonable. From the velocity profile of a simple shear flow, one can imagine that grains move principally in the direction of the flow, and based on Einstein’s theory random motion is necessary to induce particle diffusion. Hence, in granular media, from where does the randomness contribution arises to induce diffusion?
Well, that randomness it is implicitly in the shear flow. It comes from particle-particle collisions. Collisions occur at different angles and velocities, which indirectly imparts random momentum or energy transfer. It is also dependent on the temperature, viscosity, particle size, as in the molecular level. Taking the example of particle size, Wandersman E. et al  shows experimentally that the Mean Square Displacement (MSD) is inversely proportional to the particle radius. Since the slope of the MSD is the diffusivity, Wandersman et al works prove the existence of diffusivity at granular scale.
To give a better picture of the similarities that exist between the diffusivity at these two length scales, lets focus in the velocity fluctuations that occur in granular media. These fluctuations are dependent of the shear velocity, as the thermal fluctuations are dependent of temperature. Hence, both fluctuations (random behavior) depend of an energy input, which as increases, the velocity and thermal fluctuations increase and therefore diffusivity too.
As you have seen, at the granular scale, diffusivity exists and plays an important role within the mixing/segregation process of manufacture industries. Remember that 80% of the pharmaceutical, cosmetics, food and concrete process deals with granular particles without mention the mining industries, which is a 100%. Diffusivity promotes mixing of granular media, which is positive in producing homogeneous or uniform content of all its ingredients across a batch. On the contrary, controlling mixing to promote segregation, helps industries improve the design of separation process. In other words, the concept of diffusivity is a term widely used in the industries that boost their production capital. Fundamental understanding in this area not only provides money saving to the industries, but also safer products (drugs or foods) to the consumers.
Wandersman, E., Dijksman, J., and Hecke, M., Particle diffusion in slow granular bulk flow, v. 100, p. 1-6, (2012).