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This paper presents a novel semi-blind source separation approach for speech dereverberation. Based on a time independence assumption of the clean speech signals, direct sound and late reverberation are treated as separate sources and are separated using the auxiliary function based independent component analysis (Aux-ICA) algorithm. We show that the dereverberation performance is closely related to the underlying source probability density prior and the proposed approach generalizes to the popular weighted prediction error (WPE) algorithm, if the direct sound follows a Gaussian distribution with time-varying variances. The efficacy of the proposed approach is fully validated by speech quality and speech recognition experiments conducted on the REVERB Challenge dataset.