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Diver breathing sounds can be used as a characteristic for the passive detection of divers. This work introduces an approach for detecting the presence of a diver based on diver breathing sounds signals. An underwater channel model for passive diver detection is built to evaluate the impacts of acoustic energy transmission loss and ambient noise interference. The noise components of the observed signals are suppressed by spectral subtraction based on block-based threshold theory and smooth minimal statistic noise tracking theory. Then the envelope spectrum features of the denoised signal are extracted for diver detection. The performance of the proposed detection method is demonstrated through experimental analysis and numerical modeling.