That's an ugly, ugly spot for AA. About as bad as it can get. You don't even have backdoor options. Your Aces have terrible equity against their likely ranges, so for me it's an easy (though annoyed) fold.
Think we have to call with our overpairs (especially those without a diamond) or else we're overfolding. Opponent can have TT-JJ, maybe even QQ, that they might play this way. It's also a spot where villains can easily overbluff with 7x and diamond combos. Heads up I think we're calling at least two streets here, but three ways I can see calling flop/folding turn to further aggression being reasonable.