# Geometric GAN

arXiv: https://arxiv.org/abs/1705.02894 · HTML: https://mlsanity.com/paper/1705.02894/

## Key facts

- Cited by 233 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 May 2017.

## Built on by (most cited first, 30 of 233)

- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [High-Fidelity Audio Compression with Improved RVQGAN](https://mlsanity.com/paper/2306.06546/) (2023)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [StyleGAN-T: Unlocking the Power of GANs for Fast Large-Scale Text-to-Image Synthesis](https://mlsanity.com/paper/2301.09515/) (2023)
- [Projected GANs Converge Faster](https://mlsanity.com/paper/2111.01007/) (2021)
- [SinNeRF: Training Neural Radiance Fields on Complex Scenes from a Single Image](https://mlsanity.com/paper/2204.00928/) (2022)
- [Towards Faster and Stabilized GAN Training for High-fidelity Few-shot Image Synthesis](https://mlsanity.com/paper/2101.04775/) (2021)
- [High-Resolution Virtual Try-On with Misalignment and Occlusion-Handled Conditions](https://mlsanity.com/paper/2206.14180/) (2022)
- [DriveGAN: Towards a Controllable High-Quality Neural Simulation](https://mlsanity.com/paper/2104.15060/) (2021)
- [Regularizing Generative Adversarial Networks under Limited Data](https://mlsanity.com/paper/2104.03310/) (2021)
- [GANcraft: Unsupervised 3D Neural Rendering of Minecraft Worlds](https://mlsanity.com/paper/2104.07659/) (2021)
- [SANA-Sprint: One-Step Diffusion with Continuous-Time Consistency Distillation](https://mlsanity.com/paper/2503.09641/) (2025)
- [EnvEdit: Environment Editing for Vision-and-Language Navigation](https://mlsanity.com/paper/2203.15685/) (2022)
- [PD-GAN: Probabilistic Diverse GAN for Image Inpainting](https://mlsanity.com/paper/2105.02201/) (2021)
- [SceneDreamer: Unbounded 3D Scene Generation from 2D Image Collections](https://mlsanity.com/paper/2302.01330/) (2023)
- [Aligning Latent and Image Spaces to Connect the Unconnectable](https://mlsanity.com/paper/2104.06954/) (2021)
- [ToonCrafter: Generative Cartoon Interpolation](https://mlsanity.com/paper/2405.17933/) (2024)
- [Dual Contrastive Learning for Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/2104.07689/) (2021)
- [GANs for Medical Image Synthesis: An Empirical Study](https://mlsanity.com/paper/2105.05318/) (2021)
- [Composition-aware Graphic Layout GAN for Visual-textual Presentation Designs](https://mlsanity.com/paper/2205.00303/) (2022)
- [Reverse Engineering of Generative Models: Inferring Model Hyperparameters from Generated Images](https://mlsanity.com/paper/2106.07873/) (2021)
- [Rebooting ACGAN: Auxiliary Classifier GANs with Stable Training](https://mlsanity.com/paper/2111.01118/) (2021)
- [Flash Diffusion: Accelerating Any Conditional Diffusion Model for Few Steps Image Generation](https://mlsanity.com/paper/2406.02347/) (2024)
- [Stochastic Image-to-Video Synthesis using cINNs](https://mlsanity.com/paper/2105.04551/) (2021)
- [Video Seal: Open and Efficient Video Watermarking](https://mlsanity.com/paper/2412.09492/) (2024)
- [RangeLDM: Fast Realistic LiDAR Point Cloud Generation](https://mlsanity.com/paper/2403.10094/) (2024)
- [Training GANs with Stronger Augmentations via Contrastive Discriminator](https://mlsanity.com/paper/2103.09742/) (2021)
- [PERF: Panoramic Neural Radiance Field from a Single Panorama](https://mlsanity.com/paper/2310.16831/) (2023)
- [Finding an Unsupervised Image Segmenter in Each of Your Deep Generative Models](https://mlsanity.com/paper/2105.08127/) (2021)
- [Deep Learning-based Image and Video Inpainting: A Survey](https://mlsanity.com/paper/2401.03395/) (2024)

## Abstract (arXiv)

Generative Adversarial Nets (GANs) represent an important milestone for effective generative models, which has inspired numerous variants seemingly different from each other. One of the main contributions of this paper is to reveal a unified geometric structure in GAN and its variants. Specifically, we show that the adversarial generative model training can be decomposed into three geometric steps: separating hyperplane search, discriminator parameter update away from the separating hyperplane, and the generator update along the normal vector direction of the separating hyperplane. This geometric intuition reveals the limitations of the existing approaches and leads us to propose a new formulation called geometric GAN using SVM separating hyperplane that maximizes the margin. Our theoretical analysis shows that the geometric GAN converges to a Nash equilibrium between the discriminator and generator. In addition, extensive numerical results show that the superior performance of geometric GAN.