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，已有研究指出，在基于能量的框架下最大化对数似然可构建对抗性范式，其中判别器提供未归一化密度（常称为能量）。本文进一步发展该视角，引入重要性采样，并证明：1）Wasserstein GAN对配分函数的估计存在偏差，我们提出采用无偏估计量；2）优化似然时必须最大化生成器熵。我们假设这能改善模态覆盖。与以往工作不同，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及计算生成器熵项的关键。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更少，因其无需可逆函数。实验结果表明，我们的方法收敛更快，生成的样本质量与采用相似架构的GAN相当，成功避免了在常用数据集上的过拟合，并生成了训练数据的光滑低维潜在表征。