In this talk I will present strategies for detecting low energy atmospheric neutrino flux and the diffuse supernova neutrino background. The low energy atmospheric neutrinos may be detectable with distinctive nuclear signatures of exclusive neutrino-carbon interactions. The benefit of those channels is that they lead to detectable nuclear-decay signals with low backgrounds. The neutral-current signature is a line at 15.11 MeV and the charged-current signatures are two- or three-fold coincidences with delayed decays. JUNO has a chance to make the first identified measurement of sub-100 MeV atmospheric neutrinos. This study is also a step towards multi-detector studies of low-energy atmospheric neutrinos, with the goal of identifying additional distinctive nuclear signatures for carbon and other targets. Fully understanding the average core-collapse supernova requires detecting the diffuse supernova neutrino background (DSNB) in all flavors. While the electron antineutrino DSNB flux is near detection, and the electron neutrino DSNB flux has a good upper limit and prospects for improvement, the heavy flavor neutrino DSNB flux has a poor limit and heretofore had no clear path for improved sensitivity. I will show that a succession of xenon-based dark matter detectors can dramatically improve sensitivity to heavy flavor neutrino DSNB via the neutrino-nucleus coherent scattering channel. Ultimately, to reach the standard flux range significant exposures will be needed, which may be achievable with the series of proposed lead-based RES-NOVA detectors.