Fully understanding the average core-collapse supernova requires detecting the diffuse supernova neutrino background (DSNB) in all flavors. While the DSNB νe flux is near detection, and the DSNB νe flux has a good upper limit and promising prospects for improved sensitivity, the DSNB νx (each of νµ, ντ , νµ, ντ ) 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 νx the neutrino-nucleus coherent scattering channel. XENON1T could match the present sensitivity of ∼ 10 3 cm −2 s −1 per νx flavor, XENONnT would have linear improvement of sensitivity with exposure, and a long run of DARWIN could reach a flux sensitivity of ∼ 10 cm −2 s −1 . Together, these would also contribute to greatly improve bounds on non-standard scenarios. Ultimately, to reach the standard flux range of ∼ 1 cm −2 s −1 , even larger exposures will be needed, which we show may be possible with the series of proposed lead-based RES-NOVA detectors.