If a diver was deep enough that the exhaled air bubbles could collapse under the pressure of the sea water, the diver is most likely long since dead due to that same pressure.
Some insignificant gas exchange occurs on the surface of the bubble as it rises to the surface. In an aquarium the bubbler mostly works to encourage water circulation to the surface, the rising bubbles also bring water to the surface, disturbing the water surface to encourage oxygen diffusion.
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