In this paper numerical solutions of the Zabolotskaya, Khokhlov, Kuznetsov (i.e., ZKK) second‐order paraxial wave equation are used to illustrate the concept of “transverse amplitude diffusion” [G. D. Malyuzhinets, Soviet Phys. Uspekhi69, 749–758 (1959)] via the changing field structure of a diffraction‐limited parametric acoustic array. In order to establish confidence in the numerical procedure, computed solutions are first compared with analytically derived weak finite‐amplitude solutions. The amplitude‐dependent directivity of parametric arrays formed by quasisaturated and saturated primary waves is then examined by considering (i) the effect of intensity‐induced mutual coupling between adjacent ray tubes; (ii) its effect on the range‐dependent ‘diffraction’ patterns of individual spectral components; and (iii) its effect on the time waveform. Throughout the review results will be displayed by means of three‐dimensional computer graphic projections.