Air embolism and scuba diving?

The minimum depth you can emerge from is, well, zero. Strange question.

If you're free-diving you can't go down deep enough or for long enough for it to be a problem - you'd die first.

Water pressure increases with depth. The rule of thumb for divers is '10 msw (33 fsw) = 1 additional atmosphere'. So at the surface the pressure is 1 atm, at 10 msw it is 2 atm, at 20 msw it is 3 atm, at 30 msw it is 4 atm, etc.

Any sealed flexible airspace taken underwater will be compressed proportional to the external (ambient) pressure. So if you start with a balloon containing 1 litre volume at the surface, at 10 msw it will be 0.5 L, at 20 msw it will be 0.33... L, at 30 msw it will be 0.25 L, etc. Conversely, if you fill a ballon with 1 L at 30 msw, it will swell to 2 L volume by the time it gets to 10 msw (because pressure has halved from 4 to 2 atm), and 4 L volume by the time it reaches the surface.

Since apnea divers only inhale at the surface, air embolism is not a major risk for them. Their lung volume is compressed to well below 'normal' as they descend, and then re-expands to 'normal' as they regain the surface.

However, scuba gear is designed to deliver compressed breathing gas at ambient pressure: this means that there is no additional (muscular) effort required to breathe at depth. The gas breathed is most commonly air (~21%O2, 79%N2), but any mixure of non-toxic gases can be used which includes sufficient oxygen to sustain consciousness (I will use 'air' for simplicity). The deeper the dive, the greater the pressure of air being delivered to the lungs.

While the scuba diver remains at depth, breathing high pressure air does not in itself present a major mechanical problem (although there are multiple potential physiological issues with high pressure O2 and N2, which I won't go into here). However, if a diver breathes compressed air at depth, and then reascends while holding his breath (e.g. while panicking), he puts himself at very high risk of suffering some kind of barotrauma.

This is because as the diver ascends, the air volume trapped in his lungs will 'try to' expand -- like the balloon filled at depth in my example above. But because the air cannot escape through the closed windpipe it expands within the chest cavity, and will tear through the lung tissue, possibly entering the bloodstream, where bubbles may form blockages (i.e. air embolism).

The greatest 'risk space' for suffering air embolism is actually the shallowest depths, where the biggest volume change takes place -- again, see the ballon example above. It can happen during an ascent from as little as 1-2 m under the water (at 2 m, pressure is 1.2 atm, i.e. 20% higher than surface pressure.

This is one of the reasons why training/certification is required to use scuba gear safely, and why the Golden Rule of Scuba is 'Breathe continuously, and NEVER hold your breath'.