  We present the first prediction of the probability distribution function
(PDF) for self-organization of shear flows modeled by a nonlinear diffusion
equation with a stochastic forcing. A novel non-perturbative method based on a
coherent structure is utilized for the prediction of the PDFs, revealing strong
intermittency with exponential tails. Numerical simulations confirm these
results. The predicted power spectra are also in a good agreement with
simulation results. The results imply a significant probability of
supercritical states due to stochastic perturbation in a variety of systems.
