There isn't a day that goes by, that I don't receive a question on diffusion in our listening, home theater, and recording rooms. It appears many have a handle on absorption, but really do not understand diffusion. Diffusion and absorption are similar in some of the issues they address and deal with in small room acoustics, but vastly different in others.
Quadratic diffusion is the most consistent and predictable type of diffusion. A quadratic diffusor is a series of troughs or wells that are calculated to a specific depth and width based on prime numbers. The width of each well aligns itself with one half wavelength theory and each well depth aligns itself with quarter wavelength theory. The well width is about a half wavelength at the shortest wavelength to be diffused and the depths of the diffusor are calculated using a prime number as the base and applying a formula (residue calculation) to the number. Prime numbers to look at are 7, 11, 13, 17, 19 ...
A horizontally placed quadratic diffusor ( it is spelled with an "o", no matter what your spell checker says) spreads sound energy that enters it in a vertical array. A vertically positioned diffusor spreads sound energy out in a horizontal, fan like, array. These two dimensions of sound diffusion (there are only 3) combined together are powerful room acoustic tools.
Diffusion and absorption both deal with room wall reflections. Diffusion takes the reflection and "chops" it up into a group of smaller reflections if you will and then redistributes those "reflections" back into the room in a fan like array. The distributed energy back into the room is not altered in time or amplitude. Absorption reduces the amplitude of the reflection by changing some of the reflected energy to heat. Diffusors do one thing more and it is an amazing thing.
Through a blend of both horizontal and vertical diffusion in a listening room along, lets say the front wall directly behind the speakers, one can make the front wall acoustically disappear. It can also do this to the rear wall, side walls, and ceiling.
Diffusion can add depth to your sound stage. It can remove the acoustical reflections from the front wall to the listening position in a way absorption could never do. One can actually choose the amount of sound stage depth increase by selecting the appropriate prime number based diffusion sequence. Now that's an acoustical tool!
Diffusion and absorption are certainly important factors, in the design of a listening environment.
Poor people use something called an "EQ." I am a big fan of 32 band 1/3 octave EQs but most people, being poor, go for the 6-8 band.
The EQ does not make up for the lack of absorptive / reflective balance, but it creates the illusion.