# WarpedGANSpace: Finding non-linear RBF paths in GAN latent space

arXiv: https://arxiv.org/abs/2109.13357 · HTML: https://mlsanity.com/paper/2109.13357/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 37 references that are in the map.
- First posted on arXiv 27 Sep 2021.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [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)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [GANSpace: Discovering Interpretable GAN Controls](https://mlsanity.com/paper/2004.02546/) (2020)
- [Unsupervised Discovery of Interpretable Directions in the GAN Latent Space](https://mlsanity.com/paper/2002.03754/) (2020)
- [On the "steerability" of generative adversarial networks](https://mlsanity.com/paper/1907.07171/) (2019)
- [GANalyze: Toward Visual Definitions of Cognitive Image Properties](https://mlsanity.com/paper/1906.10112/) (2019)
- [S3FD: Single Shot Scale-invariant Face Detector](https://mlsanity.com/paper/1708.05237/) (2017)
- [HOPE-Net: A Graph-based Model for Hand-Object Pose Estimation](https://mlsanity.com/paper/2004.00060/) (2020)
- [Semantic Hierarchy Emerges in Deep Generative Representations for Scene Synthesis](https://mlsanity.com/paper/1911.09267/) (2019)
- [Controlling generative models with continuous factors of variations](https://mlsanity.com/paper/2001.10238/) (2020)
- [FairFace: Face Attribute Dataset for Balanced Race, Gender, and Age](https://mlsanity.com/paper/1908.04913/) (2019)
- [Image Counterfactual Sensitivity Analysis for Detecting Unintended Bias](https://mlsanity.com/paper/1906.06439/) (2019)
- [ELEGANT: Exchanging Latent Encodings with GAN for Transferring Multiple Face Attributes](https://mlsanity.com/paper/1803.10562/) (2018)
- [GAN "Steerability" without optimization](https://mlsanity.com/paper/2012.05328/) (2020)
- [A Spectral Regularizer for Unsupervised Disentanglement](https://mlsanity.com/paper/1812.01161/) (2018)
- [High-Fidelity Synthesis with Disentangled Representation](https://mlsanity.com/paper/2001.04296/) (2020)
- [OOGAN: Disentangling GAN with One-Hot Sampling and Orthogonal Regularization](https://mlsanity.com/paper/1905.10836/) (2019)
- [RPGAN: GANs Interpretability via Random Routing](https://mlsanity.com/paper/1912.10920/) (2019)

## Built on by (most cited first, 30 of 48)

- [StyleGAN-Human: A Data-Centric Odyssey of Human Generation](https://mlsanity.com/paper/2204.11823/) (2022)
- [Style-Based Global Appearance Flow for Virtual Try-On](https://mlsanity.com/paper/2204.01046/) (2022)
- [HyperReenact: One-Shot Reenactment via Jointly Learning to Refine and Retarget Faces](https://mlsanity.com/paper/2307.10797/) (2023)
- [StyleGAN knows Normal, Depth, Albedo, and More](https://mlsanity.com/paper/2306.00987/) (2023)
- [Attribute-preserving Face Dataset Anonymization via Latent Code Optimization](https://mlsanity.com/paper/2303.11296/) (2023)
- [Finding Directions in GAN's Latent Space for Neural Face Reenactment](https://mlsanity.com/paper/2202.00046/) (2022)
- [PandA: Unsupervised Learning of Parts and Appearances in the Feature Maps of GANs](https://mlsanity.com/paper/2206.00048/) (2022)
- [Personalized Image Generation with Deep Generative Models: A Decade Survey](https://mlsanity.com/paper/2502.13081/) (2025)
- [StyleMask: Disentangling the Style Space of StyleGAN2 for Neural Face Reenactment](https://mlsanity.com/paper/2209.13375/) (2022)
- [Latent Traversals in Generative Models as Potential Flows](https://mlsanity.com/paper/2304.12944/) (2023)
- [GAN-based Facial Attribute Manipulation](https://mlsanity.com/paper/2210.12683/) (2022)
- [Feature Unlearning for Pre-trained GANs and VAEs](https://mlsanity.com/paper/2303.05699/) (2023)
- [Near Perfect GAN Inversion](https://mlsanity.com/paper/2202.11833/) (2022)
- [DiffusionAct: Controllable Diffusion Autoencoder for One-shot Face Reenactment](https://mlsanity.com/paper/2403.17217/) (2024)
- [Are CLIP features all you need for Universal Synthetic Image Origin Attribution?](https://mlsanity.com/paper/2408.09153/) (2024)
- [Tensor Component Analysis for Interpreting the Latent Space of GANs](https://mlsanity.com/paper/2111.11736/) (2021)
- [Improving Fairness using Vision-Language Driven Image Augmentation](https://mlsanity.com/paper/2311.01573/) (2023)
- [ContraCLIP: Interpretable GAN generation driven by pairs of contrasting sentences](https://mlsanity.com/paper/2206.02104/) (2022)
- [Parts of Speech-Grounded Subspaces in Vision-Language Models](https://mlsanity.com/paper/2305.14053/) (2023)
- [Flow Factorized Representation Learning](https://mlsanity.com/paper/2309.13167/) (2023)
- [Make It So: Steering StyleGAN for Any Image Inversion and Editing](https://mlsanity.com/paper/2304.14403/) (2023)
- [MM2Latent: Text-to-facial image generation and editing in GANs with multimodal assistance](https://mlsanity.com/paper/2409.11010/) (2024)
- [Self-Conditioned Generative Adversarial Networks for Image Editing](https://mlsanity.com/paper/2202.04040/) (2022)
- [One-shot Neural Face Reenactment via Finding Directions in GAN's Latent Space](https://mlsanity.com/paper/2402.03553/) (2024)
- [Orthogonal SVD Covariance Conditioning and Latent Disentanglement](https://mlsanity.com/paper/2212.05599/) (2022)
- [GANravel: User-Driven Direction Disentanglement in Generative Adversarial Networks](https://mlsanity.com/paper/2302.00079/) (2023)
- [Householder Projector for Unsupervised Latent Semantics Discovery](https://mlsanity.com/paper/2307.08012/) (2023)
- [Explaining Image Classifiers Using Contrastive Counterfactuals in Generative Latent Spaces](https://mlsanity.com/paper/2206.05257/) (2022)
- [Interpreting Latent Spaces of Generative Models for Medical Images using Unsupervised Methods](https://mlsanity.com/paper/2207.09740/) (2022)
- [iWarpGAN: Disentangling Identity and Style to Generate Synthetic Iris Images](https://mlsanity.com/paper/2305.12596/) (2023)

## Abstract (arXiv)

This work addresses the problem of discovering, in an unsupervised manner, interpretable paths in the latent space of pretrained GANs, so as to provide an intuitive and easy way of controlling the underlying generative factors. In doing so, it addresses some of the limitations of the state-of-the-art works, namely, a) that they discover directions that are independent of the latent code, i.e., paths that are linear, and b) that their evaluation relies either on visual inspection or on laborious human labeling. More specifically, we propose to learn non-linear warpings on the latent space, each one parametrized by a set of RBF-based latent space warping functions, and where each warping gives rise to a family of non-linear paths via the gradient of the function. Building on the work of Voynov and Babenko, that discovers linear paths, we optimize the trainable parameters of the set of RBFs, so as that images that are generated by codes along different paths, are easily distinguishable by a discriminator network. This leads to easily distinguishable image transformations, such as pose and facial expressions in facial images. We show that linear paths can be derived as a special case of our method, and show experimentally that non-linear paths in the latent space lead to steeper, more disentangled and interpretable changes in the image space than in state-of-the art methods, both qualitatively and quantitatively. We make the code and the pretrained models publicly available at: https://github.com/chi0tzp/WarpedGANSpace.