We propose a high-resolution technique for estimating the source time function of a seismic event from only one record. This technique is based on the spectral factorization of the minimum phase wavelet from the most random part of a seismogram: its coda. As the coda non-stationarity is inconsistent with the classical spectral factorization theory, we develop a two-step algorithm: first, the diffuse coda field is whitened to remove the non-stationary attenuation effect; second, the minimum phase wavelet equivalent of the seismic source time function is estimated. Applied to the recordings of the Kursk's wreck, this method gives a source wavelet strikingly similar to the general shape of an underwater explosion, allowing us to infer its depth and yield. Based on the fundamental random character of diffusive waves, this approach opens up promising applications for new blind deconvolution methods.