# Bridging the Gap Between f-GANs and Wasserstein GANs

arXiv: https://arxiv.org/abs/1910.09779 · HTML: https://mlsanity.com/paper/1910.09779/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2019.

## Built on by (most cited first, 23 of 23)

- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [ViTGAN: Training GANs with Vision Transformers](https://mlsanity.com/paper/2107.04589/) (2021)
- [Regularizing Generative Adversarial Networks under Limited Data](https://mlsanity.com/paper/2104.03310/) (2021)
- [A General Recipe for Likelihood-free Bayesian Optimization](https://mlsanity.com/paper/2206.13035/) (2022)
- [SAN: Inducing Metrizability of GAN with Discriminative Normalized Linear Layer](https://mlsanity.com/paper/2301.12811/) (2023)
- [Self-Diagnosing GAN: Diagnosing Underrepresented Samples in Generative Adversarial Networks](https://mlsanity.com/paper/2102.12033/) (2021)
- [Single-Model Attribution of Generative Models Through Final-Layer Inversion](https://mlsanity.com/paper/2306.06210/) (2023)
- [Pseudo-Spherical Contrastive Divergence](https://mlsanity.com/paper/2111.00780/) (2021)
- [On f-Divergence Principled Domain Adaptation: An Improved Framework](https://mlsanity.com/paper/2402.01887/) (2024)
- [Moreau-Yosida f-divergences](https://mlsanity.com/paper/2102.13416/) (2021)
- [Outcome Assumptions and Duality Theory for Balancing Weights](https://mlsanity.com/paper/2203.09557/) (2022)
- [One-Line-of-Code Data Mollification Improves Optimization of Likelihood-based Generative Models](https://mlsanity.com/paper/2305.18900/) (2023)
- [Information Processing Equalities and the Information-Risk Bridge](https://mlsanity.com/paper/2207.11987/) (2022)
- [OMASGAN: Out-of-Distribution Minimum Anomaly Score GAN for Sample Generation on the Boundary](https://mlsanity.com/paper/2110.15273/) (2021)
- [Statistical Error Bounds for GANs with Nonlinear Objective Functionals](https://mlsanity.com/paper/2406.16834/) (2024)
- [MS3D: A RG Flow-Based Regularization for GAN Training with Limited Data](https://mlsanity.com/paper/2408.11135/) (2024)
- [On the Hardness of Unsupervised Domain Adaptation: Optimal Learners and Information-Theoretic Perspective](https://mlsanity.com/paper/2507.06552/) (2025)
- [Unified Perspective on Probability Divergence via Maximum Likelihood Density Ratio Estimation: Bridging KL-Divergence and Integral Probability Metrics](https://mlsanity.com/paper/2201.13127/) (2022)
- [Determination of galaxy photometric redshifts using Conditional Generative Adversarial Networks (CGANs)](https://mlsanity.com/paper/2501.06532/) (2025)
- [Concentration Inequalities for Stochastic Optimization of Unbounded Objective Functions with Application to Denoising Score Matching](https://mlsanity.com/paper/2502.08628/) (2025)
- [Style Quantization for Data-Efficient GAN Training](https://mlsanity.com/paper/2503.24282/) (2025)
- [DEMIST: Decoupled Multi-stream latent diffusion for Quantitative Myelin Map Synthesis](https://mlsanity.com/paper/2511.12396/) (2025)
- [Learning To Sample From Diffusion Models Via Inverse Reinforcement Learning](https://mlsanity.com/paper/2602.08689/) (2026)

## Abstract (arXiv)

Generative adversarial networks (GANs) have enjoyed much success in learning high-dimensional distributions. Learning objectives approximately minimize an f-divergence (f-GANs) or an integral probability metric (Wasserstein GANs) between the model and the data distribution using a discriminator. Wasserstein GANs enjoy superior empirical performance, but in f-GANs the discriminator can be interpreted as a density ratio estimator which is necessary in some GAN applications. In this paper, we bridge the gap between f-GANs and Wasserstein GANs (WGANs). First, we list two constraints over variational f-divergence estimation objectives that preserves the optimal solution. Next, we minimize over a Lagrangian relaxation of the constrained objective, and show that it generalizes critic objectives of both f-GAN and WGAN. Based on this generalization, we propose a novel practical objective, named KL-Wasserstein GAN (KL-WGAN). We demonstrate empirical success of KL-WGAN on synthetic datasets and real-world image generation benchmarks, and achieve state-of-the-art FID scores on CIFAR10 image generation.