We propose a probabilistic latent variable model for unsupervised cluster matching, which is the task of finding correspondences between clusters of objects in different domains. Existing object matching methods find one-to-one matching. The proposed model finds many-to-many matching, and can handle multiple domains with different numbers of objects. The proposed model assumes that there are an infinite number of latent vectors that are shared by all domains, and that each object is generated using one of the latent vectors and a domain-specific linear projection. By inferring a latent vector to be used for generating each object, objects in different domains are clustered in shared groups, and thus we can find matching between clusters in an unsupervised manner. We present efficient inference procedures for the proposed model based on a stochastic EM algorithm. The effectiveness of the proposed model is demonstrated with experiments using synthetic and real data sets.