The theory of ultrabroadband multifrequency Raman generation is extended, for the first time, to allow for beam-propagation effects in one and two transverse dimensions. We show that a complex transverse structure develops even when diffraction is neglected. In the general case, we examine how the ultrabroadband multifrequency Raman generation process is affected by the intensity, phase quality, and width of the input beams, and by the length of the Raman medium. The evolution of power spectra, intensity profiles, and global characteristics of the multifrequency beams are investigated and explained. In the two-dimensional transverse case, bandwidths comparable to the optical carrier frequency, spanning the whole visible spectrum and beyond, are still achievable.