We propose the infinite non-negative matrix factorization (INMF) which assumes a potentially unbounded number of components in the Bayesian xmf model. We devise an inference scheme based 011 Gibbs sampling in conjunction with Metropolis-Hastings moves that admits cross-dimensional exploration of the posterior density. The approach can effectively establish the model order for NMF at a less computational cost than existing approaches such as thermodynamic integration and existing reversible jump Markov chain Monte Carlo sampling schemes. On synthetic and real data we demonstrate the success of (INMF).