Abstract: A neural network system is provided, implementing a generative model for autoregressively generating a distribution for a plurality of current filter-bank samples of an audio signal, wherein the current samples correspond to a current time slot, and each current sample corresponds to a channel of the filter-bank. The system includes a hierarchy of a plurality of neural network processing tiers ordered from a top to a bottom tier, each tier trained to generate conditioning information based on previous filter-bank samples and, for at least each tier but the top tier, also on the conditioning information from a tier higher up in the hierarchy, and an output stage trained to generate the probability distribution based on previous samples for one or more previous time slots and the conditioning information from the lowest processing tier.