I'd imagine it'll be implemented like the current dungeon armour sets.
Say the dungeon is 4 levels.
You can do the first level with normal gear, and for doing so you get 60 tokens.
To do the 2nd level you'll need at least 1 piece of ascended gear, to get the ascended amulet you might need to get 210 tokens. So you'd have to do level one 4 times to get the tokens to get the amulet to progress to level 2.
To get to level 3 might require 3 ascended items, so you'd have to run a bunch of level 1 and level 2 to get the tokens to afford 2 ascended rings letting you access level 3.
Then to do the final stage of the dungeon you might need 5 ascended items, amulet, 2rings, and 2 earings etc.
So, you don't have to go out and get a specific set just for this dungeon, but by playing hte dungeon you earn the items you need to progress further, and also items that are better than you currently have.
It might not work like that, but to me that seems the most sensible way of implementing it.
Those that didn't want to do the dungeon never have to go there or get ascended gear, and it'd make ascended stuff soulbound so you couldn't sell them on and tank exotic prices.