Deep Generative Learning via Variational Gradient Flow

Learning the generative model, i.e., the underlying data generating distribution, based on large amounts of data is one the fundamental task in machine learning and statistics [46].Recent advances in deep generative models have provided novel techniques for unsupervised and semi-supervised learning, with broad application varying from image synthesis [44], semantic image editing [60], image-to-image translation [61] to low-level image processing [29]. Implicit deep generative model is a powerful and flexible framework to approximate the target distribution by learning deep samplers [38] including Generative adversarialnetworks (GAN) [16] and likelihood based models, such as variational auto-encoders (VAE) [23] and flow based methods [11], as their main representatives. The above mentioned implicit deep generative models focus on learning a deterministic or stochastic nonlinear mapping that can transform low dimensional latent samples from referenced simple distribution to samples that closely match the target distribution. GANs build a minmax two player game between the generator and discriminator. During the training, the generator transforms samples from a simple reference distribution into samples that would hopefully to deceive the discriminator, while the discriminator conducts a differential two-sample test to distinguish the generated samples from the observed samples. The objective of vanilla GANs amounts to the Jensen-Shannon (JS) divergence between the learned distribution and target distributions. The vanilla GAN generates sharp image samples but suffers form the instability issues [3]. A myriad of extensions to vanilla GANs have been investigated, both theoretically or empirically, in order to achieve a stable training and high quality sample generation.