Generative Adversarial Networks (GANs) can produce high-quality samples, but do not provide an estimate of the probability density around the samples. However, it has been noted that maximizing the log-likelihood within an energy-based setting can lead to an adversarial framework where the discriminator provides unnormalized density (often called energy). We further develop this perspective, incorporate importance sampling, and show that 1) Wasserstein GAN performs a biased estimate of the partition function, and we propose instead to use an unbiased estimator; 2) when optimizing for likelihood, one must maximize generator entropy. This is hypothesized to provide a better mode coverage. Different from previous works, we explicitly compute the density of the generated samples. This is the key enabler to designing an unbiased estimator of the partition function and computation of the generator entropy term. The generator density is obtained via a new type of flow network, called one-way flow network, that is less constrained in terms of architecture, as it does not require to have a tractable inverse function. Our experimental results show that we converge faster, produce comparable sample quality to GANs with similar architecture, successfully avoid over-fitting to commonly used datasets and produce smooth low-dimensional latent representations of the training data.

生成对抗网络（GANs）可以生成高质量的样本，但不能提供样本周围的概率密度估计。本文通过最大化log-likelihood来建议改进分区函数的无偏估计方法，同时最大化生成器熵以提供更好的模式覆盖，利用一种新型的流网络——单向流网络来计算生成样本的密度，从而设计出分区函数的无偏估计方法，并在实验中验证了该方法的快速收敛性、与相似结构GANs相当的样本质量、成功避免过度拟合常见数据集以及产生平滑的低维潜在数据表示。

使用单向流进行对抗性似然估计