The Origins Space Telescope is one of four flagship missions under study for the 2020 Astrophysics Decadal Survey. With a 5.9-m cold (4.5 K) telescope deployed from space, Origins promises unprecedented sensitivity in the near-, mid-, and far-infrared from 2.8 to 588  μm. This mandates the use of ultrasensitive and stable detectors in all of the Origins instruments. At the present, no known detectors can meet Origins’ stability requirements in the near- to mid-infrared or its sensitivity requirements in the far-infrared. We discuss the applicability of transition-edge sensors, as both calorimeters and bolometers, to meet these requirements, and lay out a path toward improving the present state-of-the-art.