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The present paper establishes the self-averaging, radiative transfer limit for the two-frequency Wigner distribution for random classical waves in the paraxial approximation. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a Boltzmann-like integral equation or a Fokker-Planck-like differential equation in the phase space. When the longitudinal fluctuation is dominant, the Fokker-Planck-like equation can be solved exactly. The scaling limit of the two-frequency Wigner distribution contains the asymptotic of cross-frequency correlation which determines pulse propagation in the radiative transfer regime

Self-averaging scaling limits of two-frequency Wigner distribution for random paraxial waves