Fully understanding the average core-collapse supernova requires detecting the diffuse supernova neutrino background (DSNB) in all flavors. While the DSNB flux is near detection, and the DSNB flux has a good upper limit and promising prospects for improved sensitivity, the DSNB (each of ) flux has a poor limit and heretofore had no clear path for improved sensitivity. We show that a succession of xenon-based dark matter detectors — XENON1T (completed), XENONnT (under construction), and DARWIN (proposed) — can dramatically improve sensitivity to DSNB the neutrino-nucleus coherent scattering channel. XENON1T could match the present sensitivity of per flavor, XENONnT would have linear improvement of sensitivity with exposure, and a long run of DARWIN could reach a flux sensitivity of . Together, these would also contribute to greatly improve bounds on non-standard scenarios. Ultimately, to reach the standard flux range of , even larger exposures will be needed, which we show may be possible with the series of proposed lead-based RES-NOVA detectors.