# Disconnected Manifold Learning for Generative Adversarial Networks

arXiv: https://arxiv.org/abs/1806.00880 · HTML: https://mlsanity.com/paper/1806.00880/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2018.

## Built on by (most cited first, 27 of 27)

- [Verifying the Union of Manifolds Hypothesis for Image Data](https://mlsanity.com/paper/2207.02862/) (2022)
- [MG-GAN: A Multi-Generator Model Preventing Out-of-Distribution Samples in Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2108.09274/) (2021)
- [Can Push-forward Generative Models Fit Multimodal Distributions?](https://mlsanity.com/paper/2206.14476/) (2022)
- [Textual Manifold-based Defense Against Natural Language Adversarial Examples](https://mlsanity.com/paper/2211.02878/) (2022)
- [On the expressivity of bi-Lipschitz normalizing flows](https://mlsanity.com/paper/2107.07232/) (2021)
- [Manifold Learning Benefits GANs](https://mlsanity.com/paper/2112.12618/) (2021)
- [VQ-Flows: Vector Quantized Local Normalizing Flows](https://mlsanity.com/paper/2203.11556/) (2022)
- [medXGAN: Visual Explanations for Medical Classifiers through a Generative Latent Space](https://mlsanity.com/paper/2204.05376/) (2022)
- [Partition-Guided GANs](https://mlsanity.com/paper/2104.00816/) (2021)
- [Analyzing and Improving Optimal-Transport-based Adversarial Networks](https://mlsanity.com/paper/2310.02611/) (2023)
- [Conditional Unscented Autoencoders for Trajectory Prediction](https://mlsanity.com/paper/2310.19944/) (2023)
- [Latent reweighting, an almost free improvement for GANs](https://mlsanity.com/paper/2110.09803/) (2021)
- [Emergent Asymmetry of Precision and Recall for Measuring Fidelity and Diversity of Generative Models in High Dimensions](https://mlsanity.com/paper/2306.09618/) (2023)
- [Action Hallucination in Generative Vision-Language-Action Models](https://mlsanity.com/paper/2602.06339/) (2026)
- [Multi-level Latent Space Structuring for Generative Control](https://mlsanity.com/paper/2202.05910/) (2022)
- [Unveiling the Latent Space Geometry of Push-Forward Generative Models](https://mlsanity.com/paper/2207.10541/) (2022)
- [Convergence and Recovery Guarantees of Unsupervised Neural Networks for Inverse Problems](https://mlsanity.com/paper/2309.12128/) (2023)
- [Compressing Image-to-Image Translation GANs Using Local Density Structures on Their Learned Manifold](https://mlsanity.com/paper/2312.14776/) (2023)
- [Spider GAN: Leveraging Friendly Neighbors to Accelerate GAN Training](https://mlsanity.com/paper/2305.07613/) (2023)
- [Learning Generative Prior with Latent Space Sparsity Constraints](https://mlsanity.com/paper/2105.11956/) (2021)
- [Unsupervised Image Generation with Infinite Generative Adversarial Networks](https://mlsanity.com/paper/2108.07975/) (2021)
- [Estimating Dataset Dimension via Singular Metrics under the Manifold Hypothesis: Application to Inverse Problems](https://mlsanity.com/paper/2507.07291/) (2025)
- [StegOT: Trade-offs in Steganography via Optimal Transport](https://mlsanity.com/paper/2509.11178/) (2025)
- [VARGAN: Variance Enforcing Network Enhanced GAN](https://mlsanity.com/paper/2109.02117/) (2021)
- [Backdoor Attack with Mode Mixture Latent Modification](https://mlsanity.com/paper/2403.07463/) (2024)
- [Analytical Discovery of Manifold with Machine Learning](https://mlsanity.com/paper/2504.02511/) (2025)
- [UniOD: A Universal Model for Outlier Detection across Diverse Domains](https://mlsanity.com/paper/2507.06624/) (2025)

## Abstract (arXiv)

Natural images may lie on a union of disjoint manifolds rather than one globally connected manifold, and this can cause several difficulties for the training of common Generative Adversarial Networks (GANs). In this work, we first show that single generator GANs are unable to correctly model a distribution supported on a disconnected manifold, and investigate how sample quality, mode dropping and local convergence are affected by this. Next, we show how using a collection of generators can address this problem, providing new insights into the success of such multi-generator GANs. Finally, we explain the serious issues caused by considering a fixed prior over the collection of generators and propose a novel approach for learning the prior and inferring the necessary number of generators without any supervision. Our proposed modifications can be applied on top of any other GAN model to enable learning of distributions supported on disconnected manifolds. We conduct several experiments to illustrate the aforementioned shortcoming of GANs, its consequences in practice, and the effectiveness of our proposed modifications in alleviating these issues.