# CLUE-MARK: Watermarking Diffusion Models using CLWE

arXiv: https://arxiv.org/abs/2411.11434 · HTML: https://mlsanity.com/paper/2411.11434/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Robustness, privacy and adversarial aspects, one of 14 directions in Diffusion models.
- Builds on 23 of its 50 references that are in the map.
- First posted on arXiv 18 Nov 2024.

## Placed in

- Diffusion models / [Robustness, privacy and adversarial aspects](https://mlsanity.com/diffusion/robustness-privacy-and-adversarial-aspects/)
- LLM safety and security / [Watermarking generated content and models](https://mlsanity.com/safety/watermarking-generated-content-and-models/)

## Builds on (most cited first, 23 of 23)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [HiDDeN: Hiding Data With Deep Networks](https://mlsanity.com/paper/1807.09937/) (2018)
- [The Stable Signature: Rooting Watermarks in Latent Diffusion Models](https://mlsanity.com/paper/2303.15435/) (2023)
- [StegaStamp: Invisible Hyperlinks in Physical Photographs](https://mlsanity.com/paper/1904.05343/) (2019)
- [Artificial Fingerprinting for Generative Models: Rooting Deepfake Attribution in Training Data](https://mlsanity.com/paper/2007.08457/) (2020)
- [Tree-Ring Watermarks: Fingerprints for Diffusion Images that are Invisible and Robust](https://mlsanity.com/paper/2305.20030/) (2023)
- [Gaussian Shading: Provable Performance-Lossless Image Watermarking for Diffusion Models](https://mlsanity.com/paper/2404.04956/) (2024)
- [MBRS : Enhancing Robustness of DNN-based Watermarking by Mini-Batch of Real and Simulated JPEG Compression](https://mlsanity.com/paper/2108.08211/) (2021)
- [Responsible Disclosure of Generative Models Using Scalable Fingerprinting](https://mlsanity.com/paper/2012.08726/) (2020)
- [Watermarks in the Sand: Impossibility of Strong Watermarking for Generative Models](https://mlsanity.com/paper/2311.04378/) (2023)
- [An Undetectable Watermark for Generative Image Models](https://mlsanity.com/paper/2410.07369/) (2024)
- [ReDMark: Framework for Residual Diffusion Watermarking on Deep Networks](https://mlsanity.com/paper/1810.07248/) (2018)
- [No Free Lunch in LLM Watermarking: Trade-offs in Watermarking Design Choices](https://mlsanity.com/paper/2402.16187/) (2024)
- [On Exact Inversion of DPM-Solvers](https://mlsanity.com/paper/2311.18387/) (2023)
- [Continuous LWE](https://mlsanity.com/paper/2005.09595/) (2020)
- [PTW: Pivotal Tuning Watermarking for Pre-Trained Image Generators](https://mlsanity.com/paper/2304.07361/) (2023)
- [Continuous LWE is as Hard as LWE & Applications to Learning Gaussian Mixtures](https://mlsanity.com/paper/2204.02550/) (2022)
- [Steganalysis on Digital Watermarking: Is Your Defense Truly Impervious?](https://mlsanity.com/paper/2406.09026/) (2024)
- [Hybrid blind robust image watermarking technique based on DFT-DCT and Arnold transform](https://mlsanity.com/paper/1911.00753/) (2019)

## Built on by (most cited first, 1 of 1)

- [Proof-of-Authorship for Diffusion-based AI Generated Content](https://mlsanity.com/paper/2603.17513/) (2026)

## Abstract (arXiv)

As AI-generated images become widespread, reliable watermarking is essential for content verification, copyright enforcement, and combating disinformation. Existing techniques rely on heuristic approaches and lack formal guarantees of undetectability, making them vulnerable to steganographic attacks that can expose or erase the watermark. Additionally, these techniques often degrade output quality by introducing perceptible changes, which is not only undesirable but an important barrier to adoption in practice. In this work, we introduce CLUE-Mark, the first provably undetectable watermarking scheme for diffusion models. CLUE-Mark requires no changes to the model being watermarked, is computationally efficient, and because it is provably undetectable is guaranteed to have no impact on model output quality. Our approach leverages the Continuous Learning With Errors (CLWE) problem -- a cryptographically hard lattice problem -- to embed watermarks in the latent noise vectors used by diffusion models. By proving undetectability via reduction from a cryptographically hard problem we ensure not only that the watermark is imperceptible to human observers or adhoc heuristics, but to any efficient detector that does not have the secret key. CLUE-Mark allows multiple keys to be embedded, enabling traceability of images to specific users without altering model parameters. Empirical evaluations on state-of-the-art diffusion models confirm that CLUE-Mark achieves high recoverability, preserves image quality, and is robust to minor perturbations such JPEG compression and brightness adjustments. Uniquely, CLUE-Mark cannot be detected nor removed by recent steganographic attacks.