  Non-autoregressive text to speech (NAR-TTS) models have attracted much
attention from both academia and industry due to their fast generation speed.
One limitation of NAR-TTS models is that they ignore the correlation in time
and frequency domains while generating speech mel-spectrograms, and thus cause
blurry and over-smoothed results. In this work, we revisit this over-smoothing
problem from a novel perspective: the degree of over-smoothness is determined
by the gap between the complexity of data distributions and the capability of
modeling methods. Both simplifying data distributions and improving modeling
methods can alleviate the problem. Accordingly, we first study methods reducing
the complexity of data distributions. Then we conduct a comprehensive study on
NAR-TTS models that use some advanced modeling methods. Based on these studies,
we find that 1) methods that provide additional condition inputs reduce the
complexity of data distributions to model, thus alleviating the over-smoothing
problem and achieving better voice quality. 2) Among advanced modeling methods,
Laplacian mixture loss performs well at modeling multimodal distributions and
enjoys its simplicity, while GAN and Glow achieve the best voice quality while
suffering from increased training or model complexity. 3) The two categories of
methods can be combined to further alleviate the over-smoothness and improve
the voice quality. 4) Our experiments on the multi-speaker dataset lead to
similar conclusions as above and providing more variance information can reduce
the difficulty of modeling the target data distribution and alleviate the
requirements for model capacity.
