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; and 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 a tractable inverse function. Our experimental results show that our method converges faster, produces comparable sample quality to GANs with similar architecture, successfully avoids over-fitting to commonly used datasets and produces smooth low-dimensional latent representations of the training data.

翻译：生成对抗网络（GANs）能够生成高质量样本，但无法提供样本周围的概率密度估计。然而已有研究表明，在基于能量的框架中最大化对数似然可引出一个对抗性框架，其中判别器提供非归一化密度（通常称为能量）。我们进一步拓展这一视角，引入重要性采样，并证明：1）Wasserstein GAN对配分函数存在有偏估计，我们提出改用无偏估计量；2）在优化似然时需最大化生成器熵，这被假设能提供更好的模态覆盖。与先前工作不同，我们显式计算生成样本的密度，这是设计配分函数无偏估计量和计算生成器熵项的关键支撑。生成器密度通过一种新型流网络——称为单向流网络——获得，该网络在架构上约束较少，因而不需要可逆的逆函数。实验结果表明，我们的方法收敛更快，能产生与相似架构GANs相当的样本质量，成功避免了对常用数据集的过拟合，并生成了训练数据的平滑低维潜在表征。