This paper describes novel methods for diffuse noise suppression using crystal-shaped microphone arrays. The two-stage processing of the observed signals by the Minimum Variance Distortionless Response (MVDR) beamformer and the subsequent Wiener post-filter is effective for diffuse noise suppression and gives the linear minimum mean square error (LMMSE) estimator of the target signal. It is essential in this framework to accurately estimate the short-time power spectrum and the steering vectors of the target signal from the noisy observations. Our methods diagonalize the spatial noise covariance matrix and utilizes the denoised off-diagonal entries of the spatial covariance matrix to accurately estimate the short-time power spectrum and the steering vectors of the target signal. We employ crystal arrays, certain classes of crystal-shaped array geometries, which make it possible to diagonalize the unknown noise covariance matrix by a constant unitary matrix regardless of its value as long as noise meets an isotropy condition. It is shown through experiments with simulated and real environmental noise that the proposed methods outperform previous methods substantially for real world noise and in the presence of reverberation.