Interesting article at Greatest.com discusses why athletes seem to be better at handling pain than the general population. According to the article, athletes do tolerate pain better than the general population, but they don't really have an answer as to why. Two plausible answers are that this tolerance is learned over time and that an increase in exercise intensity causes the release of endorphin (the body's natural pain releaver) which then reduces that pain.
How does this relate to diving. Well, when you think of diving and pain the first thing that comes to my mind is a big 'ole smack! Now I'm not sure but I don't think there are enough endorphins in the world to alleviate a face plant off 10-meter, but I can attest to the fact that after multiple smacks they don't seem to bother you as much. So I am voting for the learned over time theory.
Another interesting point from the article is that there are two strategies used to deflect that pain. One is to concentrate on the specifics of the task, known as association. The other is to think of something positive (happy thoughts, happy thoughts) as a distraction, known as dissociation. I'm not sure how much dissociation will help a diver. You have only a few seconds to concentrate until you hit the water so I don't think it is a good idea to be distracted. I vote for association in this instance.
All in all, an interesting read.