Branson, who was on the show to promote his Virgin American airline, did a segment with Colbert and doused him with a glass of water when the segment ended.
He was reportedly angry (or pretending to be angry) because he didn't have a chance to plug the airline by name.
Colbert then retaliated by drenching Branson after sending a staffer for a glass of water. Colbert had to be dried off by staffers after the water fight.
Comedy Central officials claim it was all in good fun. But audience members who attended the taping last Tuesday blogged that Colbert looked ruffled and angry afterward — and that the two men sat in stony silence for a few seconds.