Following the loss of the Hitomi x-ray astronomy satellite shortly after its launch in early 2016, the US and Japanese space agencies (NASA and JAXA) agreed to fund a replacement mission, presently called the X-Ray Imaging and Spectroscopy Mission (XRISM). XRISM will include only the two soft x-ray instruments from Hitomi, the Soft X-ray Spectrometer (SXS), and the Soft X-ray Imager (SXI). The spectrometer instrument, now named Resolve, will be similar to the original SXS design. It consists of a 6 by 6 array of silicon microcalorimeters cooled to 50 millikelvin by means of a 3-stage Adiabatic Demagnetization Refrigerator (ADR) whose operation is supported by a 40 liter superfluid helium tank, a 4.5-degrees-Kelvin Joule-Thomson cryocooler and a number of 2-stage Stirling cryocoolers. These components were all successfully demonstrated on Hitomi before its failure. This talk will summarize the design of the XRISM ADR and how it differs from the SXS version.