We rep the diamond draw here, so unless he wants to bet out when the draw hits, the diamond face cards are bluff outs for us.

By floating and betting an ace, we might get a hand like TT or JJ to fold which may otherwise not fold to a flop raise. We don't really want to commit that many chips on a bluff. The downside to floating is that we do end up giving him a free card that could beat us. The upside is that it's generally safer as iopq stated, we lose less than we would with a raise on the flop. We also get more information from our villain for approximately the same price as we would with a flop raise, since we get to see whether he will barrel again or check. Also, betting after he checks turn is a lot safer than raising the flop since we can narrow his range further.

Of course, you won't be floating as routinely against villains who 2 barrel a lot. But without reads, I think floating then taking the pot away on the turn is a decent line that capitalizes on our position.