# Rewriting Geometric Rules of a GAN

arXiv: https://arxiv.org/abs/2207.14288 · HTML: https://mlsanity.com/paper/2207.14288/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 69 of its 89 references that are in the map.
- First posted on arXiv 28 Jul 2022.

## Builds on (most cited first, 30 of 69)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Semantic Image Synthesis with Spatially-Adaptive Normalization](https://mlsanity.com/paper/1903.07291/) (2019)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [FaceForensics++: Learning to Detect Manipulated Facial Images](https://mlsanity.com/paper/1901.08971/) (2019)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [StyleCLIP: Text-Driven Manipulation of StyleGAN Imagery](https://mlsanity.com/paper/2103.17249/) (2021)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [CNN-generated images are surprisingly easy to spot... for now](https://mlsanity.com/paper/1912.11035/) (2019)
- [Encoding in Style: a StyleGAN Encoder for Image-to-Image Translation](https://mlsanity.com/paper/2008.00951/) (2020)
- [GANSpace: Discovering Interpretable GAN Controls](https://mlsanity.com/paper/2004.02546/) (2020)
- [Designing an Encoder for StyleGAN Image Manipulation](https://mlsanity.com/paper/2102.02766/) (2021)
- [Leveraging Frequency Analysis for Deep Fake Image Recognition](https://mlsanity.com/paper/2003.08685/) (2020)
- [Video-to-Video Synthesis](https://mlsanity.com/paper/1808.06601/) (2018)
- [Differentiable Augmentation for Data-Efficient GAN Training](https://mlsanity.com/paper/2006.10738/) (2020)

## Built on by (most cited first, 25 of 25)

- [Multi-Concept Customization of Text-to-Image Diffusion](https://mlsanity.com/paper/2212.04488/) (2022)
- [Erasing Concepts from Diffusion Models](https://mlsanity.com/paper/2303.07345/) (2023)
- [Ablating Concepts in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2303.13516/) (2023)
- [DragDiffusion: Harnessing Diffusion Models for Interactive Point-based Image Editing](https://mlsanity.com/paper/2306.14435/) (2023)
- [Label-Free Concept Bottleneck Models](https://mlsanity.com/paper/2304.06129/) (2023)
- [Drag Your GAN: Interactive Point-based Manipulation on the Generative Image Manifold](https://mlsanity.com/paper/2305.10973/) (2023)
- [Editing Implicit Assumptions in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2303.08084/) (2023)
- [Wear-Any-Way: Manipulable Virtual Try-on via Sparse Correspondence Alignment](https://mlsanity.com/paper/2403.12965/) (2024)
- [Customizing Text-to-Image Models with a Single Image Pair](https://mlsanity.com/paper/2405.01536/) (2024)
- [ReFACT: Updating Text-to-Image Models by Editing the Text Encoder](https://mlsanity.com/paper/2306.00738/) (2023)
- [StableDrag: Stable Dragging for Point-based Image Editing](https://mlsanity.com/paper/2403.04437/) (2024)
- [Discovering Transferable Forensic Features for CNN-generated Images Detection](https://mlsanity.com/paper/2208.11342/) (2022)
- [DiffUHaul: A Training-Free Method for Object Dragging in Images](https://mlsanity.com/paper/2406.01594/) (2024)
- [LightningDrag: Lightning Fast and Accurate Drag-based Image Editing Emerging from Videos](https://mlsanity.com/paper/2405.13722/) (2024)
- [A Survey on Deep Generative 3D-aware Image Synthesis](https://mlsanity.com/paper/2210.14267/) (2022)
- [Domain Expansion of Image Generators](https://mlsanity.com/paper/2301.05225/) (2023)
- [Towards Smooth Video Composition](https://mlsanity.com/paper/2212.07413/) (2022)
- [Continual Unlearning for Foundational Text-to-Image Models without Generalization Erosion](https://mlsanity.com/paper/2503.13769/) (2025)
- [Content-Based Search for Deep Generative Models](https://mlsanity.com/paper/2210.03116/) (2022)
- [DragGaussian: Enabling Drag-style Manipulation on 3D Gaussian Representation](https://mlsanity.com/paper/2405.05800/) (2024)
- [Taming Normalizing Flows](https://mlsanity.com/paper/2211.16488/) (2022)
- [Dynamically Masked Discriminator for Generative Adversarial Networks](https://mlsanity.com/paper/2306.07716/) (2023)
- [Low-Rank Adaptation of Neural Fields](https://mlsanity.com/paper/2504.15933/) (2025)
- [Sketch2Human: Deep Human Generation with Disentangled Geometry and Appearance Control](https://mlsanity.com/paper/2404.15889/) (2024)
- [AI and the creative realm: A short review of current and future applications](https://mlsanity.com/paper/2306.01795/) (2023)

## Abstract (arXiv)

Deep generative models make visual content creation more accessible to novice users by automating the synthesis of diverse, realistic content based on a collected dataset. However, the current machine learning approaches miss a key element of the creative process -- the ability to synthesize things that go far beyond the data distribution and everyday experience. To begin to address this issue, we enable a user to "warp" a given model by editing just a handful of original model outputs with desired geometric changes. Our method applies a low-rank update to a single model layer to reconstruct edited examples. Furthermore, to combat overfitting, we propose a latent space augmentation method based on style-mixing. Our method allows a user to create a model that synthesizes endless objects with defined geometric changes, enabling the creation of a new generative model without the burden of curating a large-scale dataset. We also demonstrate that edited models can be composed to achieve aggregated effects, and we present an interactive interface to enable users to create new models through composition. Empirical measurements on multiple test cases suggest the advantage of our method against recent GAN fine-tuning methods. Finally, we showcase several applications using the edited models, including latent space interpolation and image editing.