  This paper proposes an approach to the joint modeling of the short-time
Fourier transform magnitude and phase spectrograms with a deep generative
model. We assume that the magnitude follows a Gaussian distribution and the
phase follows a von Mises distribution. To improve the consistency of the phase
values in the time-frequency domain, we also apply the von Mises distribution
to the phase derivatives, i.e., the group delay and the instantaneous
frequency. Based on these assumptions, we explore and compare several
combinations of loss functions for training our models. Built upon the
variational autoencoder framework, our model consists of three convolutional
neural networks acting as an encoder, a magnitude decoder, and a phase decoder.
In addition to the latent variables, we propose to also condition the phase
estimation on the estimated magnitude. Evaluated for a time-domain speech
reconstruction task, our models could generate speech with a high perceptual
quality and a high intelligibility.
