This paper proposes a general enhancement to the Normalizing Flows (NF) used in neural vocoding. As a case study, we improve expressive speech vocoding with a revamped Parallel Wavenet (PW). Specifically, we propose to extend the affine transformation of PW to the more expressive invertible non-affine function. The greater expressiveness of the improved PW leads to better-perceived signal quality and naturalness in the waveform reconstruction and text-to-speech (TTS) tasks. We evaluate the model across different speaking styles on a multi-speaker, multi-lingual dataset. In the waveform reconstruction task, the proposed model closes the naturalness and signal quality gap from the original PW to recordings by $10%$, and from other state-of-the-art neural vocoding systems by more than $60%$. We also demonstrate improvements in objective metrics on the evaluation test set with L2 Spectral Distance and Cross-Entropy reduced by $3%$ and $6unicode{x2030}$ comparing to the affine PW. Furthermore, we extend the probability density distillation procedure proposed by the original PW paper, so that it works with any non-affine invertible and differentiable function.
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