A method performed by one or more computers, the method comprising: obtaining a phoneme sequence , the phoneme sequence comprising a respective phoneme token at each of a plurality of input time steps; processing the phoneme sequence using an encoder neural network to generate a hidden representation of the phoneme sequence; generating , from the hidden representation, a conditioning input ; initializing a current waveform output , the initializing comprising sampling each of a plurality of initial values for the current waveform output from a corresponding noise distribution; and generating a final waveform output that defines an utterance of the phoneme sequence by a speaker by updating the current waveform output at each of a plurality of iterations until a termination criteria is met, wherein each iteration corresponds to a respective noise level , and wherein the updating comprises, at each iteration: processing a model input for the iteration comprising (i) the current waveform output and (ii) the conditioning input using a noise estimation neural network that is configured to process the model input to generate a noise output , wherein the noise output comprises a respective noise estimate for each value in the current waveform output; and updating the current waveform output using the noise estimate and the noise level for the iteration, the updating comprising: generating an update for the iteration from at least the noise estimate and the noise level corresponding to the iteration; and subtracting the update from the current waveform output. obtaining a phoneme sequence , the phoneme sequence comprising a respective phoneme token at each of a plurality of input time steps; processing the phoneme sequence using an encoder neural network to generate a hidden representation of the phoneme sequence; generating , from the hidden representation, a conditioning input ; initializing a current waveform output , the initializing comprising sampling each of a plurality of initial values for the current waveform output from a corresponding noise distribution; and generating a final waveform output that defines an utterance of the phoneme sequence by a speaker by updating the current waveform output at each of a plurality of iterations until a termination criteria is met, wherein each iteration corresponds to a respective noise level , and wherein the updating comprises, at each iteration: processing a model input for the iteration comprising (i) the current waveform output and (ii) the conditioning input using a noise estimation neural network that is configured to process the model input to generate a noise output , wherein the noise output comprises a respective noise estimate for each value in the current waveform output; and updating the current waveform output using the noise estimate and the noise level for the iteration, the updating comprising: generating an update for the iteration from at least the noise estimate and the noise level corresponding to the iteration; and subtracting the update from the current waveform output. processing a model input for the iteration comprising (i) the current waveform output and (ii) the conditioning input using a noise estimation neural network that is configured to process the model input to generate a noise output , wherein the noise output comprises a respective noise estimate for each value in the current waveform output; and updating the current waveform output using the noise estimate and the noise level for the iteration, the updating comprising: generating an update for the iteration from at least the noise estimate and the noise level corresponding to the iteration; and subtracting the update from the current waveform output. generating an update for the iteration from at least the noise estimate and the noise level corresponding to the iteration; and subtracting the update from the current waveform output. <EOS>