[The_Bends]

Ouch, horrible situation to be in. The preflop, flop and turn actions would seem to sit your opponent with a flush (likely an A high flush, smaller flushes woudl be worried about the fourth d and would raise the flop) but there are plenty of other hands to consider. Firstly the pot s heads up, that means that he doesn't have to be as scared of the flush as he would in a multiway, after all you raised he's only worried about AK/Qs. Without a good read you can't really put him on an overpair (he'd have RR preflop), he could however have Jacks which just made trips (probably with the Jd). AdXo is also a possiblity although I'd have to have a read to believe my opp held that and CR me.

So basically its 4:1 to call but I can't think of any hands that play this way that you beat. However you fill up 20% of the time. This combined with the possiblity this is an A high FD semi-bluff or a lower set make me inclinded to unhappily call. On the river (assuming the opp pushes) I'd fold it if I didn't improve and call with a FH. If I was checked to I'd check behind regardless.