Diffusion in fluctuative medium

We consider diffusion in a medium with randomly fluctuating diffusion coefficient. An equation is derived for diffusate concentration averaged over dimensions exceeding those of fluctuations. In the case when fluctations are weak and their correlation scales small the equation is reduced to a differential one, where the effective diffusion coefficient is always lower than the average one. A stability criterion for uniform distribution of diffusate is derived. Some implications of the theory for the radiation effects in solids are discussed.