We propose efficient algorithms for jointly estimating the power spectrogram and the room transfer functions of a target signal for blind suppression of diffuse noise. The estimated parameters are utilized for designing a multichannel Wiener filter for suppressing diffuse noise. To unify existing models of diffuse noise, we propose a linear algebraic framework, where we specify each model as a subspace spanned by the spatial covariance matrix of diffuse noise in a matrix linear space. This framework is utilized for deriving two algorithms based on covariance matrix fitting for joint estimation of the power spectrogram and the room transfer functions for the general noise model. These methods are efficient, significantly reducing the number of iterations required for obtaining reliable estimates compared to our previous technique. We compare the noise suppression performance of the proposed methods and a conventional method on real-world data.