# Correlation-Aware and Gaussianity-Preserving Robust Latent Angular Watermarking for Diffusion Models

arXiv: https://arxiv.org/abs/2607.22386 · HTML: https://mlsanity.com/paper/2607.22386/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Robustness, privacy and adversarial aspects, one of 14 directions in Diffusion models.
- Builds on 27 of its 37 references that are in the map.
- First posted on arXiv 24 Jul 2026.

## 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, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [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)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [Learned Image Compression with Discretized Gaussian Mixture Likelihoods and Attention Modules](https://mlsanity.com/paper/2001.01568/) (2020)
- [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)
- [Tree-Ring Watermarks: Fingerprints for Diffusion Images that are Invisible and Robust](https://mlsanity.com/paper/2305.20030/) (2023)
- [Robust Invisible Video Watermarking with Attention](https://mlsanity.com/paper/1909.01285/) (2019)
- [Invisible Image Watermarks Are Provably Removable Using Generative AI](https://mlsanity.com/paper/2306.01953/) (2023)
- [RingID: Rethinking Tree-Ring Watermarking for Enhanced Multi-Key Identification](https://mlsanity.com/paper/2404.14055/) (2024)
- [An Undetectable Watermark for Generative Image Models](https://mlsanity.com/paper/2410.07369/) (2024)
- [Deep Model Intellectual Property Protection via Deep Watermarking](https://mlsanity.com/paper/2103.04980/) (2021)
- [AquaLoRA: Toward White-box Protection for Customized Stable Diffusion Models via Watermark LoRA](https://mlsanity.com/paper/2405.11135/) (2024)
- [ROBIN: Robust and Invisible Watermarks for Diffusion Models with Adversarial Optimization](https://mlsanity.com/paper/2411.03862/) (2024)
- [A Watermark-Conditioned Diffusion Model for IP Protection](https://mlsanity.com/paper/2403.10893/) (2024)
- [GaussMarker: Robust Dual-Domain Watermark for Diffusion Models](https://mlsanity.com/paper/2506.11444/) (2025)
- [Semantic Watermarking Reinvented: Enhancing Robustness and Generation Quality with Fourier Integrity](https://mlsanity.com/paper/2509.07647/) (2025)
- [RAW: A Robust and Agile Plug-and-Play Watermark Framework for AI-Generated Images with Provable Guarantees](https://mlsanity.com/paper/2403.18774/) (2024)
- [FreqMark: Invisible Image Watermarking via Frequency Based Optimization in Latent Space](https://mlsanity.com/paper/2410.20824/) (2024)
- [Erase and Repair: An Efficient Box-Free Removal Attack on High-Capacity Deep Hiding](https://mlsanity.com/paper/2308.01512/) (2023)
- [Box-Free Model Watermarks Are Prone to Black-Box Removal Attacks](https://mlsanity.com/paper/2405.09863/) (2024)
- [Removing Box-Free Watermarks for Image-to-Image Models via Query-Based Reverse Engineering](https://mlsanity.com/paper/2507.18034/) (2025)

## Abstract (arXiv)

Latent domain watermarking for diffusion models embeds watermarks directly into the latent prior, enjoying non-intrusiveness to model parameters and seamless integration with the generation process. However, due to the violation of latent Gaussianity or sensitivity to normal and malicious perturbations during latent inversion, existing methods are prone to watermark detection or removal attacks. A further overlooked problem is the violation of the i.i.d. latent condition after watermarking, which leads to latent correlation degradation and generation fidelity loss. Although this has been externally measured by FID, the internal correlation structure has yet to be rigorously characterized. To address the above issues, and motivated by the rotation-invariant property of isotropic Gaussian, we propose textitLatent Angular Watermarking (LAW), which encodes watermark bits as antipodal angles (±π/2 relative to a reference pair) between disjoint pairs of latent elements while preserving the Gaussianity. The antipodal (π-separation) encoding maximizes geometric separation between bit values, and we prove that the decoding angular-error variance is proportional to the norm of the latent pair, i.e., operatornamevar(Deltaφ) propto 1/ρ2. We further propose a magnitude-driven variant, LAW-M, which anchors watermark bits in the most geometrically stable latent dimensions, yielding additional robustness gains. Theoretically, we provide a rigorous characterization of the induced correlation degradation, deriving in closed form the autocorrelation structure of the watermarked latent and proving that correlations are confined to a sparse, structured set of off-diagonal elements with fixed ±π/4 values.