High-level knowledge of language helps the human auditory system understand speech with missing information such as missing frequency bands. The automatic speech recognition community has shown that the use of this knowledge in the form of language models is crucial to obtaining high quality recognition results. In this paper, we apply this idea to the bandwidth expansion problem to automatically estimate missing frequency bands of speech. Specifically, we use language models to constrain the recently proposed non negative hidden Markov model for this application. We compare the proposed method to a bandwidth expansion algorithm based on non-negative spectrogram factorization and show improved results on two standard signal quality metrics.