Probabilistic models of audio spectrograms used in audio source separation often rely on Poisson or multinomial noise models corresponding to the generalized Kullback-Leibler (GKL) divergence popular in methods using Nonnegative Matrix Factorization (NMF). This noise model works well in practice, but it is difficult to justify since these distributions are technically only applicable to discrete counts data. This issue is particularly problematic in hierarchical and non-parametric Bayesian models where estimates of uncertainty depend strongly on the likelihood model. In this paper, we present a hierarchical Bayesian model that retains the flavor of the Poisson likelihood model but yields a coherent generative process for continuous spectrogram data. This model allows for more principled, accurate, and effective Bayesian inference in probabilistic NMF models based on GKL.