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We propose a model-based source separation system for use on single channel speech mixtures where the precise source characteristics are not known a priori. We do this by representing the space of source variation with a parametric signal model based on the eigenvoice technique for rapid speaker adaptation. We present an algorithm to infer the characteristics of the sources present in a mixture, allowing for significantly improved separation performance over that obtained using unadapted source models. The algorithm is evaluated on the task defined in the 2006 Speech Separation Challenge  and compared with separation using source-dependent models.