Apparatus for distilling a fluid such as water includes a vessel and heat transfer plates within the vessel structures to form at least one each cooling channel, evaporative channel, and condensing channel. Air enters the vessel and passes through the cooling channel, where it is cooled due to evaporation taking place in an adjacent evaporative channel. In the evaporative channel, input fluid is supplied to the walls of the heat transfer plates facing into the evaporative channel and evaporation forms vapor. The vapor is condensed in a condensing channel. In some versions of the apparatus, an evaporation channel forms a vacuum chamber and a condensing channel forms a compression chamber.