Yes, there are a number of conditions that cause velopharyngeal insufficiency (how's THAT for the phrase of the day?). Specifically, cleft palate (a hole in the roof of the mouth) or cases of palate dysfunction that may be seen after palate surgery or adenoid surgery. These patients have difficulty keeping air from escaping up through the VP valve in the back of the airway during speech, formed by the palate sealing against the back of the throat. Because of this, they have "hypernasal" speech (a sort of whiny, high pitched sound) and may occasionally have nasal regurgitation (which many of us have had if we laugh while drinking, and have liquid come out of the nose). This is mainly an issue when they try to close the valve during speech - try making a "k" sound and you will feel your palate closing against the back of your throat...
However, I would think that even in cases of an real cleft palate, it would be possible to learn the techniques of SCUBA diving - I haven't heard about this before, but I don't believe that you rely on your VP valve to keep from losing air out of your nose while diving. If that were the case, you would need to constantly be making the "k" sound during diving. If you think about how you breathe with a regulator, you really are controlling airflow by pressure changes, not by closing your VP valve.
If there is a steady stream of bubbles during both inhalation and exhalation, I would ensure good mask fit and technique before assuming that this was a palate problem. But you never know, maybe this is something that I haven't seen before!
Best,
Mike