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.

Photo-realistic visualization and animation of expressive human faces have been a long standing challenge. On one end of the spectrum, 3D face modeling methods provide parametric control but tend to generate unrealistic images, while on the other end, generative 2D models like GANs (Generative Adversarial Networks) output photo-realistic face images, but lack explicit control. Recent methods gain partial control, either by attempting to disentangle different factors in an unsupervised manner, or by adding control post hoc to a pre-trained model. Trained GANs without pre-defined control, however, may entangle factors that are hard to undo later. To guarantee some disentanglement that provides us with desired kinds of control, we train our generative model conditioned on pre-defined control parameters. Specifically, we condition StyleGAN2 on FLAME, a generative 3D face model. However, we found out that a naive conditioning on FLAME parameters yields rather unsatisfactory results. Instead we render out geometry and photo-metric details of the FLAME mesh and use these for conditioning instead. This gives us a generative 2D face model named GIF (Generative Interpretable Faces) that shares FLAME's parametric control. Given FLAME parameters for shape, pose, and expressions, parameters for appearance and lighting, and an additional style vector, GIF outputs photo-realistic face images. To evaluate how well GIF follows its conditioning and the impact of different design choices, we perform a perceptual study. The code and trained model are publicly available for research purposes at https://github.com/ParthaEth/GIF.