Generative Adversarial Network (GAN) has been widely used to generate impressively plausible data. However, it is a non-trivial task to train the original GAN model in practice due to the vanishing gradient problem. This is because the JS divergence could be a constant (i.e., log2) when original data distribution and generated data distribution hold a negligible overlapping area. Under such a scenario, the gradient of generator is 0. Most efforts have been devoted to designing a more proper difference measure while few attentions have been paid to the former aspect of the issue.

In this paper, we propose a new method to design a noise distribution having a guaranteed non-negligible overlapping area with raw data distribution. The key idea is to transform the noise from the randomized space into the raw data space. We propose to obtain the transformation as the basis matrix in non-negative matrix factorization because the basis matrix has the underlying features of the raw data. The proposed idea is instantiated as Sketch-then-Edit GAN (SEGAN) where sketches are the noises after transformation and are adopted as the name since they contains basic features of the raw data. Moreover, a new generator for editing the sketches into realistic-like data is designed. We mathematically prove that SEGAN solves the gradient vanishing problem, and conduct extensive experiments on the MNIST, CIFAR10, SVHN and Celeba datasets to demonstrate the effectiveness of SEGAN.

生成对抗网络（GAN）已被广泛用于生成令人印象深刻的可信数据。但是，由于梯度问题的消失，在实践中训练原始GAN模型是一项艰巨的任务。这是因为当原始数据分布和生成的数据分布具有可忽略的重叠区域时，JS散度可能是一个常数（即log2）。在这种情况下，生成器的梯度为0。大多数努力致力于设计一种更合适的差异度量，而很少关注该问题的前一个方面。

在本文中，我们提出了一种新的设计噪声分布的方法，该噪声分布具有保证的原始数据分布具有不可忽略的重叠区域。关键思想是将噪声从随机空间转换为原始数据空间。我们建议将变换作为非负矩阵分解中的基础矩阵，因为基础矩阵具有原始数据的基础特征。提议的想法被实例化为Sketch-then-Edit GAN（SEGAN），其中草图是变换后的噪声，由于其包含原始数据的基本特征，因此被用作名称。此外，设计了一种新的生成器，用于将草图编辑为逼真的数据。我们用数学方法证明SEGAN解决了梯度消失问题，并在MNIST，CIFAR10，