# Riemannian-Geometric Fingerprints of Generative Models

arXiv: https://arxiv.org/abs/2506.22802 · HTML: https://mlsanity.com/paper/2506.22802/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 73 references that are in the map.
- First posted on arXiv 28 Jun 2025.

## Builds on (most cited first, 30 of 44)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [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)
- [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)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [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)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [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)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Least Squares Generative Adversarial Networks](https://mlsanity.com/paper/1611.04076/) (2016)
- [CNN-generated images are surprisingly easy to spot... for now](https://mlsanity.com/paper/1912.11035/) (2019)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [Watch your Up-Convolution: CNN Based Generative Deep Neural Networks are Failing to Reproduce Spectral Distributions](https://mlsanity.com/paper/2003.01826/) (2020)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Adversarial Latent Autoencoders](https://mlsanity.com/paper/2004.04467/) (2020)
- [StyleSwin: Transformer-based GAN for High-resolution Image Generation](https://mlsanity.com/paper/2112.10762/) (2021)
- [Fourier Spectrum Discrepancies in Deep Network Generated Images](https://mlsanity.com/paper/1911.06465/) (2019)
- [A Tale of Tails: Model Collapse as a Change of Scaling Laws](https://mlsanity.com/paper/2402.07043/) (2024)

## Built on by (most cited first, 8 of 8)

- [Copyright Protection for Large Language Models: A Survey of Methods, Challenges, and Trends](https://mlsanity.com/paper/2508.11548/) (2025)
- [Are Robust LLM Fingerprints Adversarially Robust?](https://mlsanity.com/paper/2509.26598/) (2025)
- [SPRINT: Robust Model Attribution of Generated Images via Secret Pixel Reconstruction](https://mlsanity.com/paper/2508.05691/) (2025)
- [Smudged Fingerprints: A Systematic Evaluation of the Robustness of AI Image Fingerprints](https://mlsanity.com/paper/2512.11771/) (2025)
- [Causal Fingerprints of AI Generative Models](https://mlsanity.com/paper/2509.15406/) (2025)
- [Contact Wasserstein Geodesics for Non-Conservative Schr"odinger Bridges](https://mlsanity.com/paper/2511.06856/) (2025)
- [RGSQ: Riemannian Geometry-Sensitive Quantization for Large Vision-Language Models](https://mlsanity.com/paper/2609.25492/) (2026)
- [Can Pixels Alone Reveal Image Origin? Minimax Limits and Learnable Interfaces for Passive Provenance](https://mlsanity.com/paper/2609.30997/) (2026)

## Abstract (arXiv)

Recent breakthroughs and rapid integration of generative models (GMs) have sparked interest in the problem of model attribution and their fingerprints. For instance, service providers need reliable methods of authenticating their models to protect their IP, while users and law enforcement seek to verify the source of generated content for accountability and trust. In addition, a growing threat of model collapse is arising, as more model-generated data are being fed back into sources (e.g., YouTube) that are often harvested for training ("regurgitative training"), heightening the need to differentiate synthetic from human data. Yet, a gap still exists in understanding generative models' fingerprints, we believe, stemming from the lack of a formal framework that can define, represent, and analyze the fingerprints in a principled way. To address this gap, we take a geometric approach and propose a new definition of artifact and fingerprint of GMs using Riemannian geometry, which allows us to leverage the rich theory of differential geometry. Our new definition generalizes previous work (Song et al., 2024) to non-Euclidean manifolds by learning Riemannian metrics from data and replacing the Euclidean distances and nearest-neighbor search with geodesic distances and kNN-based Riemannian center of mass. We apply our theory to a new gradient-based algorithm for computing the fingerprints in practice. Results show that it is more effective in distinguishing a large array of GMs, spanning across 4 different datasets in 2 different resolutions (64 by 64, 256 by 256), 27 model architectures, and 2 modalities (Vision, Vision-Language). Using our proposed definition significantly improves the performance on model attribution, as well as a generalization to unseen datasets, model types, and modalities, suggesting its practical efficacy.