From
"Acoustic Absorbers and Diffusers - Theory, Design and Application" by Trevor J. Cox and Peter D'Antonio, pages 27-28:
"Figure 2.4 shows the effect of adding surface roughness to disperse the reflection. In this case, the semicylinder is used. It can be seen that the reflected wavefront is no longer planar, but is now semicircular. The semicircle has generated a virtual point source at the center of itself. Consequently, a semicylinder will generate spatial dispersion. The wavefronts generated are still very ordered; however, so although semicylinders are good at spatial dispersion, they are not the best diffusers because temporal dispersion is not achieved...
...A Schroeder diffuser changes the phase of the reflected wavefronts. The waves radiated by the secondary sources are complicated, and it is difficult to pick out clear cut wavefronts. As well as generating spatial dispersion, reflection phase grating diffusers generate temporal dispersion."
For those who are listening and actually care...