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.

翻译：生成对抗网络（GAN）能够产生高质量的样本，但无法提供样本周围概率密度的估计。然而，已有研究发现，在基于能量的框架中最大化对数似然会导致生成对抗框架，其中判别器提供非归一化密度（通常称为能量）。我们进一步拓展了这一视角，引入重要性采样，并表明：1）Wasserstein GAN对配分函数进行了有偏估计，我们提出改用无偏估计量；2）在优化似然时，必须最大化生成器熵。这一策略有望更好地覆盖模式。与以往工作不同，我们显式计算了生成样本的密度。这是设计配分函数无偏估计量及计算生成器熵项的关键基础。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，因为它无需具备可逆函数。实验结果表明，我们收敛更快，生成的样本质量与采用类似架构的GAN相当，成功避免了对常用数据集的过拟合，并产生了训练数据的光滑低维潜在表示。