Suppose that you build an underwater power plant which generated electricity from a hydrothermal vent [link].
Instead of sending that power to the shore using long expensive cables, I propose an alternative: Hydrogen balloons.
The method would be as follows:
One would first purify some seawater
using reverse osmosis. No energy would be needed to pressurize the seawater, since it's already at very high pressure due to the depth at which we're working.
We do need to pump the fresh water away from the R.O. membrane, but this shouldn't take much energy.
Once we have pure fresh water, we perform electrolysis on it, producing hydrogen and oxygen. The oxygen is discarded into the ambient sea water. The hydrogen is pumped into a balloon. The balloon's initial state is a flat roll of plastic, taking up relatively little space on board the power plant.
As the H2 balloon fills, we also fill a small secondary balloon with seawater (by preference using some of the brine discharged by the reverse osmosis process, but any seawater will do).
When enough H2 has been put into the first balloon, we seal the two balloons, link them with a tether, and release them.
They float up to the surface, and the water balloon acts as an anchor, to keep the hydrogen balloon from escaping into the atmosphere.
A ship finds the two balloons, aided by the beacon that's on the hydrogen balloon. The crew reels the upper balloon in, and compresses the hydrogen into a storage tank. The crew also takes the lower balloon, first piercing it and discarding the seawater that was within it. Then they set sail for shore.