illconditioned, a diffuse sound field is built up from the reflections in a room. The sound is bouncing off the walls (literally) as well as the floor, ceiling, people, furnishings, etc., and with each bounce there is some attenuation because some of the sound energy turns into miniscule amounts of heat. The thing is, this happens very unevenly at different frequencies, with high frequencies being absorbed more than midrange frequencies in general. Even just traveling through the air, the losses are a little greater at high frequencies, but the main high-frequency losses come from absorption when sound is reflected.
Add to this the fact that an omnidirectional microphone isn't omnidirectional at these same high frequencies--if you want flat response on axis, you pay for it with rolled-off response off-axis. The standard frequency response curves which the manufacturers all print are free-field response curves, meaning that they show the microphone's frequency response for sound arriving as "plane waves" on the 0-degree axis of the microphone. Move 30 degrees to the right or left, however, and the picture changes considerably at high frequencies. That information is contained in the polar response graphs which, unfortunately, not very many people know how to read (but it's not actually hard to figure out, and HUGELY worth learning).
There is no typical environment that produces an ideally diffuse sound field in the sense that an anechoic chamber offers an ideally direct (free) sound field. You can approach it in some large Gothic cathedrals where the sound hangs around in the air for six or seven seconds after a singer has already let go of a note, but it is a theoretical construct as is the perfect anechoic chamber (real ones all have limits and problems).
I'm not very familiar with DPA's product line so give me a moment to go look. Or better yet, let me tell you what I would be looking for, and then I don't have to go look. If this is a microphone of the more or less usual diameter for a small-diaphragm condenser, then it will show an on-axis elevation of several dB (5 - 6 - 7 - 8) at around 8 - 9 - 10 - 11 kHz if it is a diffuse-field type. (For smaller microphone diameters the frequency range would be higher.) A free-field type will always have flat high frequency response on axis; in a sense no one cares about its off-axis response since essentially no sound is reaching it from off-axis anyway.
If the microphone is made to be extremely small then these distinctions will no longer matter within the audible range. That may seem like the ideal, but it's not--because such small microphones have rather high equivalent noise levels and anyway, most engineers seem to find that their recordings sound better with some directionality in the microphones at high frequencies, though I suppose that could vary with the circumstances and with people's personal tastes (he said, trying to avoid any arguments with Earthworks users).
I hope this answers your questions to some extent.
--best regards