I am pretty sure that the naked clowns were produced by selective breeding. Ocellaris clowns with very little white were bred and the babies that had the least amount of white were bred and so on. Even now only a small portion of a single spawn have little enough white to be sold as "naked clowns". These fish are not necessarily inbred.
The picasso clowns come from one original wild caught percula male that had extreme "picasso" markings. He was paired with an onyx perc female. The babies that most resembled the original male were then used to produce more picasso babies. Wild caught picasso clowns still turn up every once in a while, but I don't think that ORA has incorporated any in their breeding program. If they have not, then the picasso clowns are all inbred off the same original male, however inbreeding did not cause the markings, it is just used to produce more individuals with the similar markings.
Snowflakes were originally marketed by Tropic Marin in England. These fish reportedly come from a normal pair of ocellaris that just happen to produce a few snowflake babies in each of their spawns. Snowflake bred to snowflake produces a good percentage of snowflake babies. The ORA line comes from the Tropic Marin snowflakes. All snowflakes can be traced back to the original two normal looking wild caught parents (so they are inbred), but again, the inbreeding did not cause the color pattern, it is just the easiest way to perpetuate it.
We used to have an ORA employee on this list, but I haven't seen him for awhile. If I have misspoken I hope that he can correct me.