Hi all,
Here is a little thing I stumbled upon after many hours of playing. Maybe all of you already know it and I'm just a bit slow, but I just bring it to general attention anyhow.

The Diadem of the Savant is a circlet which is tagged as light armor. This with good reason:

Arenea Ienith, the priestess of Azura, wears a hooded robe; it is not possible to replace it with another robe. She will also wear armor, but only if given a helmet. Therefore it is impossible to ever see her with her head uncovered (as far as I know).

Here the Diadem of the Savant comes in: Since it is technically a helmet, she will wear it and thereby uncover her head. And now a pleasant surprise: she looks gorgeous. The best looking Dunmer in Skyrim.

I suppose there are other followers with the same problem, probably all mages. Therefore I think the entry in the elderscroll.wikia is not correct when it mentions that this double nature (robe/light armor) of the diadem is a bug. It makes perfect sense for players who want to know how mage-NPC really look.

If anyone knows of other in-game means to permanently uncover the head of hooded NPCs, please let me know.

The Diadem will respawn if it is found on a stump close to Froki's Shack. The reward for successfully finishing the Labrynth in Labyrnthian is a second Diadem, it is on the Daedra you have to kill.

Where did you get this?

If you give the mages a bunch of circlets and robes they randomly equip them when entering/leaving new areas. Saving and reloading also switches their gear around. I gave Brelyna a circlet I enchanted and she chose it over the other circlets in her inventory, though she sometimes equips the ones that are not enchanted. I gave her two magic robes and she switches between them. I don't think its got to do with the value of the item or the enchantment, its just random. Leaving only one circlet sometimes makes her equip her default hood, so again random.

Of course you could go the 100 skill in pickpocketing (Perfect Touch) route and just remove their gear and place the items you want. The thing is you'll have to leave at least one piece of their starting gear like the boots in order for your new items to be considered the new 'default' gear.

And I agree about Aranea though its better off to give her an enchanted circlet of Magicka/waterbreathing, since those are the only head enchantments that work on followers. The diadem will only give the meager armor bonus.

However the diadem has the advantage that it stays. I have Aranea in enchanted scaled armour and the diadem, and she never takes it off or switches her gear. The diadem my be rather weak, but she is powerfull enough to make up for it in my experience.

you're talking about the college quest to labrynthian? if so i didnt get the diadem, i got a priest mask and random loot

also isnt the diadem from shivering isles?

The Labrynth is Shalidors Maze, The entrance is in Labrynthian behind the room that held the masks of the Dragon Priests.
I do not remember if a similiarly named or enchanted item was in SI

I gave Arenea Lenith light dragon armor to wear. she wore it with her head uncovered. I also gave her forsworn armor to wear. hello sixy. Not sure what your trying to do but she'll get out of those robes. (or you can steal them off her haha)

I came across a witch in a tower near Riftin. I helped her kill her mother... I then stole her robe cause I wanted to see her face. I then took her has a companion to follow me which she did in her underwear. I felt bad leaving her alone in the tower without anything to protect her so I gave her a powerful robe to wear. she put it on cause it was better then what she had equipted which was nothing.