Unlike typical diffusion, anomalous diffusion is described by a power law, where  is the so-called generalized diffusion coefficient and  is the elapsed time. The classes of anomalous diffusions are classified as follows:
* α < 1: subdiffusion. This can happen due to crowding or walls. For example, a random walker in a crowded room, or in a maze, is able to move as usual for small random steps, but cannot take large random steps, creating subdiffusion. This appears for example in protein diffusion within cells, or diffusion through porous media. Subdiffusion has been proposed as a measure of macromolecular crowding in the cytoplasm. 
* α = 1: Brownian motion.
* : superdiffusion. Superdiffusion can be the result of active cellular transport processes or due to jumps with a heavy-tail distribution.
* α = 2: ballistic motion. The prototypical example is a particle moving at constant velocity: .
* : hyperballistic. It has been observed in optical systems.
In 1926, using weather balloons, Lewis Fry Richardson demonstrated that the atmosphere exhibits super-diffusion. In a bounded system, the mixing length (which determines the scale of dominant mixing motions) is given by the Von Kármán constant according to the equation , where  is the mixing length,  is the Von Kármán constant, and  is the distance to the nearest boundary. Because the scale of motions in the atmosphere is not limited, as in rivers or the subsurface, a plume continues to experience larger mixing motions as it increases in size, which also increases its diffusivity, resulting in super-diffusion.