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An acoustically diffusing surface is one that scatters sound in all directions rather than giving a single 'specular' reflection like a mirror.
This scattering of sound gives a good mix of sound and is particularly beneficial for music as it allows the listener to feel enveloped in the sound. In classical concert halls, a diffuse sound field was provided by the architectural modelling and stucco work. The acoustical benefits of this were not understood at the time and this was a complete stroke of luck on the designers part. In more modern spaces, diffusion is provided by specilaist acoustic diffusers.
Diffusion makes a space sound bigger and so is useful in smaller rooms such as recording studios. It is also beneficial in regular shaped rooms to help break up standing waves / room modes.