I had previously thought of CHIM as very obscure secret knowledge - conceived by Lorkhan, and kept secret even from the gods. I was surprised when I started to notice how many of the Daedra are mentioned in conjunction with it.

Vivec claims to have first learned of CHIM from Molag Bal http://www.imperial-library.info/content/36-lessons-vivec

The teachings that sparked off of the Psijic Endeavor, i.e. gaining CHIM, are credited to Mephala, Boethiah, Azura, Trinimac, and Lorkhan (who is Padomaic in spite of being an Aedra) http://www.imperial-library.info/content/more-psijic-endeavor

Azura recognizes CHIM in Vivec during the trial http://www.imperial-library.info/content/trial-vivec

CHIM is the subject of Vol. 3 of the Mythic Dawn commentaries, written by Mankar Camoran, the servant of Mehrunes Dagon. http://www.imperial-library.info/content/mythic-dawn-commentaries-vol-3

So how is this such widespread knowledge among the Daedra despite the fact that none of them have achieved it? Furthermore, what motive do they have in imparting this knowledge to mortals? (i.e. to Vivec, to Camoran, and to Veloth)

Is CHIM only achievable by mortals? (seems likely) Are the Daedra secretly interested in helping to achieve "The final subgradient of AE"? And finally, as agents of stasis are the Aedra opposed to this goal or ignorant of it?

Azura wasn't at the trial. That was a doppelganger of some kind created by Vehk to stoke his own ego and send a rude message to the goddess.
/validspeculation

As I understand, that's a matter of debate. Even so, she's one of the daedra credited with shaping Veloth's philosophies, so the point stands.

True, the point stands, and it's an interesting point. I've seen the CHIM referenced by Molag and Azura, but I somehow hadn't put it together with Mehrunes' Commentaries. It's strange that the Daedra should be so consistently involved with this concept. What's their interest in it? Does their understanding of the mortal potential for transcendence have something to do with their predilection for collecting mortal souls? Does that mortal potential have something to do with the nature of mortal souls as fragments of the dead Aedra, as differed from Daedric souls being fragments of living principalities? I think these are questions worth asking.

"Is CHIM only achievable by mortals" No but some believe it's easier to achieve with "limitations" placed upon them. So in other words mortals probably have an easier time at it. Well that probably would have been Lorkhan's view anyway.

As I understand, the existence of CHIM is "common" ish knowledge, but its achievement is a real puzzle to most. Why is it mortals are much more CHIM-capable? Because they are a perfect blend of stasis and change, their existence is revolt. The easiest way to see this is to imagine a mountain, the higher you are the better your chances of achieving CHIM, at the bottom of one side: Aedra, at the bottom of the other: Daedra, between both and on the peak: Mortal. Aedra and Daedra are pidgeon-holed into their roles, good or bad, they are stuck as what they are or in the case of aedra, as we believe them to be (which is what seriously hampers and donkey-kicks their chances of reaching CHIM to oblivion). Now for Daedra, understand they were never part of creation and are only nosing about for their own power, they are each of them a despicable aspect of a personality given form. Literally the various paths that one horrible aspect of a personality can take (the easiest example being sheogorath, as seen in shivering isles, manic, or depressive, all the various ways that madness has of manifesting itself). The problem is, so stuck they are in this role, and in this aspect, not to mention always in rivalry with something somewhere somehow, they will never be able to reach CHIM. So they steal souls, each with their various temptations and ways depending on the nasty aspect they represent. Granted some do do it for [censored] and giggles (sanguine) but they know whats going on nonetheless. They take souls to empower themselves and make sure mortals do not surpass them (Example: Azura not wanting mortals to use the tools of kag. Eat a dike you hag, oh wait...). "For even gods dislike absolutes, for it stinks of something greater than they"