The generator model assumes that the observed example is generated by a low-dimensional latent vector via a top-down network, and the latent vector follows a simple and known prior distribution, such as uniform or Gaussian white noise distribution. While we can learn an expressive top-down network to map the prior distribution to the data distribution, we can also learn an expressive prior model instead of assuming a given prior distribution. This follows the philosophy of empirical Bayes where the prior model is learned from the observed data. We propose to learn an energy-based prior model for the latent vector, where the energy function is parametrized by a very simple multi-layer perceptron. Due to the low-dimensionality of the latent space, learning a latent space energy-based prior model proves to be both feasible and desirable. In this paper, we develop the maximum likelihood learning algorithm and its variation based on short-run Markov chain Monte Carlo sampling from the prior and the posterior distributions of the latent vector, and we show that the learned model exhibits strong performance in terms of image and text generation and anomaly detection.

通过在生成模型的潜在空间中学习基于能量的模型（EBM），从而使EBM成为先验模型，该模型建立在生成模型的自上而下网络之上。通过最大似然联合学习，可以同时学习潜在空间的EBM和自上而下网络，并涉及从潜在向量的先验和后验分布中进行短程MCMC采样。由于潜在空间的低维度和自上而下网络的表现力，简单的潜在空间EBM可以有效地捕捉数据中的规律，并且潜在空间中的MCMC采样效率高且混合良好，表现出良好的图像和文本生成和异常检测能力。

学习潜空间能量先验模型