We study spin relaxation and diffusion in an electron-spin ensemble of nitrogen impurities in diamond at low temperature (0.25-1.2 K) and polarizing magnetic field (80-300 mT). Measurements exploit field-controlled coupling of the ensemble to two modes of a transmission-line resonator. The observed temperature-independent spin relaxation time indicates that spin outdiffusion across the mode volume dominates over spin-lattice relaxation. Depolarization of one hyperfine-split subensemble by pumping of another indicates fast cross relaxation, with implications for the use of subensembles as independent quantum memories.