The first part of the present theory is devoted to the derivation of a Fokker-Planck equation. The eddies smaller than the hydrodynamic scale of the diffusion cloud form a diffusivity, while the inhomogeneous, bigger eddies give rise to a nonuniform migratory drift. This introduces an eddyinduced shear which reflects on the large-scale diffusion. The eddy-induced shear does not require the presence of a permanent wind shear and is intrinsic to the diffusion. Secondly, a transport theory of diffusivity is developed by the method of repeated-cascade and is based upon a relaxation of a chain of memories with decreasing information. The cutoff is achieved by a randomization which brings statistical equilibrium. The number of surviving links varies in accordance with the number of subranges composing the spectrum. Since the intrinsitc shear provides a production subrange added to the inertia subrange, the full range of diffusion consists of inertia, composite and shear subranges. The theory predicts a variance σ2~t3, t12/5 and t2 and an eddy diffusivity K~l4/3, l7/6 for the above diffusions. The coefficients are evaluated. Comparison with experiments in the upper atmosphere and oceans is made.