requires text to perform inpainting.

#### **Audio synthesis.**

is to generate audios either unconditionally or based on given cues. A pioneering work is WaveNet [@oord2016wavenet] which achieves longer-range dependency with enlarged receptive fields through dilated convolution. Yet, one drawback for direct generation of audio samples through auto-regressive structures is its low speed. Hence, many work have since built upon it to improve the generation speed. Still under auto-regressive structure, WaveRNN [@kalchbrenner2018efficient] substitutes RNN for the stack of convolutions in [@oord2016wavenet]. Another prevalent approach is to generate an intermediate spectrogram before converting it to the final audio [@prenger2019waveglow; @donahue2018adversarial].

![image](model_architecture.pdf){width="\linewidth"}

Though the goal of audio synthesis is different than that of audio inpainting, they could both generate audios conditionally. Hence, we consider Waveglow [@prenger2019waveglow] as one of the baselines and train the vocoder to generate inpainted audio given a masked spectrogram instead of a complete one.

Proposed Method
===============

Definition
----------

For audio inpainting, we take an input audio sequence $\{A_t  \mid  t=1 \dots n\}$ with a mask $\{M_t  \mid  t=i \dots j, 1<i<j<n\}$ as input. The masked samples are set to be zeros. The model will recover the masked samples and generate the output audio $\{O_t  \mid  t=1 \dots n\}$, 