There's a system used in highrises that approach the problem from above. I once saw a floor under construction, or rather under improvement.

The floors were concrete. Some layers, maybe 1/2" total thickness, of a flexible plastic foam sheet were placed on the floor. Then there was about a half inch of standard floor underlayment, finished by 3/4" wood flooring.

I offer this because there IS an answer, though the cost of that may be more than you can spend for what you need. It kind of makes you ask yourself just how important it is, though. (I mean, this building... I watched for a couple of minutes one day while a crane lifted a grand piano to at least the 10th floor. They landed it on the patio and shoved it inside, then went to work reassembling the wall between the patio and the living room. Now THAT had a budget!)