Let me see if I can dissect this, first off say I have AA with Ad in this spot, do I always have to be continuing on this flop? What second best hands continue to a 60% pot value bet here, AQ and KK obviously so we have 6 combos that give us value, 3 combos that have us crushed (QQ) and a bunch of combos which cant continue on this flop but can value bet when hands like AdKc pick up equity. Can we not check back here to protect our range and get second best hands to lead out on what is realistically a pretty dry board when you consider our blockers, what draws can V have here? All nut flushes and KQd are impossible for him to have, KJd seems a little (read: very) optimistic to flat out of position. Does checking back really polarize our own range to exactly AK and sets?

Back to the actual hand, from his spot I think it's really unlikely to be up against AK without the diamond, so when he's calling here the bottom of my range being AdKx is freerolling 20% to river the flush, he's even drawing pretty thin to the most likely hands to turn into bluffs like JJ with a diamond. I think I would wanna throw some ranges into equilab and see what it spits out after I post this;

I think it's a really interesting spot, and I think if his call is breakeven or slightly profitable it's extremely thin and extremely high variance given stack depth which did factor into the shove. We did agree on the spot that in a vacuum the call likely isn't profitable but I do appreciate different angles on it that might change my opinion