Actually since this is a rather *hopeful* dream of mine I can tell you that it's possible, have to go through an awful lot to be able to but *possible*.
When talking to my TX doctor about it he said after a period of 5 years after my transplant I will be tested, PFT's, and a whole bunch of other tests to make sure everything is good, working order, etc. After that, if everything is in tip top shape, I can then discuss it with a dive instructor with regulations placed on me, i.e. a certain diving depth, extremely diligent of the rules, etc.
It might not be possible for me, depending on how well I'm doing in another 3 years or so but if my PFTs and everything else turn out alright then hopefully I can dive. I don't want to become certified or anything such as that but maybe go down to the caribbean and dive once or twice would be awesome enough for me. Of course that was just with my Dallas transplant doctor. Since I have moved my new doctor might say no. So... I don't know I'm just passing on info that my original TX doctor gave me.