We consider source coding of audio signals with the help of a generative model. We use a construction where a waveform is first quantized, yielding a finite bitrate representation. The waveform is then reconstructed by random sampling from a model conditioned on the quantized waveform. The proposed coding scheme is theoretically analyzed. Using SampleRNN as the generative model, we demonstrate that the proposed coding structure provides performance competitive with state-of-the-art source coding tools for specific categories of audio signals.