Abstract: Methods and apparatus for desalination of salt water (and purification of polluted water) are disclosed. Salt (or otherwise polluted) water is pumped to a desalination installation and down to the base of a desalination fractionation column, where it is mixed with hydrate-forming gas to form either positively buoyant or negatively buoyant (assisted buoyancy) hydrate. The hydrate rises or is carried upward and dissociates (melts) into the gas and pure water. In preferred embodiments, residual salt water which is heated by heat given off during formation of the hydrate is removed from the system to create a bias towards overall cooling as the hydrate dissociates endothermically at shallower depths. In preferred embodiments, the input water is passed through regions of dissociation in heat-exchanging relationship therewith so as to be cooled sufficiently for hydrate to form at pressure-depth.