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Human hearing is robust to noise, but the basis of this robustness is poorly understood. Several lines of evidence are consistent with the idea that the auditory system adapts to sound components that are stable over time, potentially achieving noise robustness by suppressing noise-like signals. Yet background noise often provides behaviorally relevant information about the environment and thus seems unlikely to be completely discarded by the auditory system. Motivated by this observation, we explored whether noise robustness might instead be mediated by internal models of noise structure that could facilitate the separation of background noise from other sounds. We found that detection, recognition, and localization in real-world background noise were better for foreground sounds positioned later in a noise excerpt, with performance improving over the initial second of exposure to a noise. These results are consistent with both adaptation-based and model-based accounts (adaptation increases over time and online noise estimation should benefit from acquiring more samples). However, performance was also robust to interruptions in the background noise and was enhanced for intermittently recurring backgrounds, neither of which would be expected from known forms of adaptation. Additionally, the performance benefit observed for foreground sounds occurring later within a noise excerpt was reduced for recurring noises, suggesting that a noise representation is built up during exposure to a new background noise and then maintained in memory. These findings suggest that noise robustness is supported by internal models—“noise schemas”—that are rapidly estimated, stored over time, and used to estimate other concurrent sounds.