This paper proposes a joint training method to learn both the variational auto-encoder (VAE) and the latent energy-based model (EBM). The joint training of VAE and latent EBM are based on an objective function that consists of three Kullback-Leibler divergences between three joint distributions on the latent vector and the image, and the objective function is of an elegant symmetric and anti-symmetric form of divergence triangle that seamlessly integrates variational and adversarial learning. In this joint training scheme, the latent EBM serves as a critic of the generator model, while the generator model and the inference model in VAE serve as the approximate synthesis sampler and inference sampler of the latent EBM. Our experiments show that the joint training greatly improves the synthesis quality of the VAE. It also enables learning of an energy function that is capable of detecting out of sample examples for anomaly detection.

本文提出一种联合训练方法，从而学习变分自动编码器（VAE）和潜在基于能量模型（EBM）。该联合训练方法基于一个客观函数，其中包括三个关于潜空间和图像的共同分布的 Kulback-Leibler 分歧，从而无缝集成多样化和对抗性学习。实验表明，这种联合训练极大地提高了 VAE 的综合质量，也使得学习能够检测异常的能量函数成为可能。

变分自编码器和潜在能量模型的联合训练