Development of scattered radiation in the geometry of a double phase-conjugate mirror is investigated numerically in the framework of a two-dimensional model that accounts for both diffraction and noncollinearity of the interacting beams. The large-scale structure of the scattered beams is found to be distorted because of the convective flow of energy out of the interaction region. We show that the output characteristics of the double phase-conjugate mirror depend strongly on the level of seed radiation in the direction of the scattered beams. The seed radiation may be due to incoherent scattering of the pumping beams inside the medium or to self-broadening of the pumping beams' spectra because of nonlinear self-interaction.