In this paper, we propose a method for estimating the azimuths of multiple sound sources accurately even in the presence of diffuse noise. MUSIC (MUltiple SIgnal Classification) for the estimation of the azimuths of multiple sources is robust against spatially white noise but the estimation performance degrades in the presence of diffuse noise. Based on a low-rank assumption on the covariance matrix of directional signals and the assumption that the covariance matrix of diffuse noise belongs to a subspace in a matrix space, the proposed method estimates the covariance matrix of the directional signals and applies MUSIC to the estimated matrix. The subspace model on the covariance matrix of diffuse noise includes as special cases noise models such as spatially uncorrelated noise, noise with a given coherence matrix, and isotropic noise observed with a crystal array. We showed through experiments with real-world noise recordings that the proposed method estimated the azimuths of multiple sources more accurately than the conventional MUSIC.