Methods, systems, and apparatus, including computer programs encoded on computer storage media, for coding speech using neural networks. One of the methods includes obtaining a bitstream of parametric coder parameters characterizing spoken speech; generating, from the parametric coder parameters, a conditioning sequence; generating a reconstruction of the spoken speech that includes a respective speech sample at each of a plurality of decoder time steps, comprising, at each decoder time step: processing a current reconstruction sequence using an auto-regressive generative neural network, wherein the auto-regressive generative neural network is configured to process the current reconstruction to compute a score distribution over possible speech sample values, and wherein the processing comprises conditioning the auto-regressive generative neural network on at least a portion of the conditioning sequence; and sampling a speech sample from the possible speech sample values.