Speech probability distribution

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A Survey on Neural Speech Synthesis (2021, background): “Modeling the one-to-many mapping under the regular L1 loss [83, 354] without enough input information will cause over-smoothing mel-spectrogram prediction [347, 328], e,g.”
On the multivariate Laplace distribution (2006, background): “Several authors have studied the statistics of speech signals in various transform domains and found the coefﬁcients to have sparse, heavy-tailed distributions [4], [5].”
Revisiting Over-Smoothness in Text to Speech (2022, methodology): “12We choose Laplace distribution as the mixture distribution since the distribution of the magnitude of spectrogram is Laplacian (Tits et al., 2019; Usman et al., 2018; Gazor and Zhang, 2003).”
Probabilistic Modeling of Speech in Spectral Domain using Maximum Likelihood Estimation (2018, background): “The following findings have been reported in [1]: The time domain representation of speech signals follows the Laplace distribution, when the silence intervals (pauses in speech) are omitted.”