Flow-GAN: Combining Maximum Likelihood and Adversarial Learning in Generative Models

TL;DR

Flow-GAN introduces an invertible generator to GANs, enabling exact likelihood computation while preserving efficient sampling. This allows a direct, quantitative comparison between maximum likelihood estimation and adversarial training on MNIST and CIFAR-10. The study finds that adversarial training delivers high-fidelity samples but very poor held-out likelihoods, while MLE provides strong density estimates but less realistic samples; a hybrid objective can balance the two. The results highlight the limitations of approximate log-likelihood estimators like AIS/KDE for implicit models and reveal Jacobian conditioning as a key factor in likelihood behavior, motivating future hybrid optimization.

Abstract

Adversarial learning of probabilistic models has recently emerged as a promising alternative to maximum likelihood. Implicit models such as generative adversarial networks (GAN) often generate better samples compared to explicit models trained by maximum likelihood. Yet, GANs sidestep the characterization of an explicit density which makes quantitative evaluations challenging. To bridge this gap, we propose Flow-GANs, a generative adversarial network for which we can perform exact likelihood evaluation, thus supporting both adversarial and maximum likelihood training. When trained adversarially, Flow-GANs generate high-quality samples but attain extremely poor log-likelihood scores, inferior even to a mixture model memorizing the training data; the opposite is true when trained by maximum likelihood. Results on MNIST and CIFAR-10 demonstrate that hybrid training can attain high held-out likelihoods while retaining visual fidelity in the generated samples.

Figures (8)

• Figure 1: Samples generated by Flow-GAN models with different objectives for MNIST (top) and CIFAR-10 (bottom).
• Figure 2: Learning curves for negative log-likelihood (NLL) evaluation on MNIST (top, in nats) and CIFAR (bottom, in bits/dim). Lower NLLs are better.
• Figure 3: Gaussian Mixture Models outperform adversarially learned models on both held-out log-likelihoods and sampling metrics on CIFAR-10 (green shaded region).
• Figure 4: CDF of the singular values magnitudes for the Jacobian of the generator functions trained on MNIST.
• Figure 5: Sample quality curves during training.