Normally, in a desalination plant, you have feed water entering a membrane at a pressure P_feed. Brine comes out at P_brine and permeate (the desalinated output) at P_permeate. P_feed is very high, P_brine is nearly as high as P_feed, and P_permeate is much lower. The flow rate of the feed and brine is considerably higher than the permeate, and one tries to adjust the parameters to get the permeate flow rate as high as possible for a given feed rate because obtaining feed water is expensive and disposing of brine is expensive.
One can engage in trickery. There’s a very clever device called a pressure exchanger that uses the large P_brine to help pressurize some of the incoming feed water. One might imagine a simpler hack of making P_permeate negative so that the feed and brine could be at low pressure, but that’s not going to work (water will not remain liquid at excessively low pressure, and negative pressure has all kinds of problems).
Now move the whole device deep under water. The feed water is (a) all around you and (b) already at plenty of pressure to let P_feed be the ambient pressure. You need to pump feed water in or brine water out to get P_feed - P_brine to be correct, but no pesky pressure exchanger is needed. You need to pump the permeate out — one might think of pumping it “up”, but really the only hard work is producing the pressure difference P_feed - P_permeate or so — water is buoyant to an extent that almost exactly negates its weight. (You’re moving the permeate up, but the pressure difference between the plant and the air helps you out. This is just like how swimming from the bottom of a pool to the surface while carrying your entire body weight is easy, while you almost certainly could not swim well enough to lift your body weight entirely above the water.)
For bonus points, it seems likely that one could dispose of the brine water immediately outside the plant on whichever side is downstream relative to the ocean currents.