I remember as a kid I wrote a report on desalination plants that were being designed at the time. Taking cold water from the depth and as it warmed it would create steam which was used to generate electricity to run the plant, and then the condensation was captured as fresh water. Or something like that.
If you read through the article that I cited, there's some discussion about various measures used to increase the efficiency and reduce/recover energy usage. The numbers I cited were the ultimate usage, for the largest amount (and highest efficiency).
There are some new developments that may reduce the energy requirements for desalination, but they are still in the lab.