# Semantic Watermarking Reinvented: Enhancing Robustness and Generation Quality with Fourier Integrity

arXiv: https://arxiv.org/abs/2509.07647 · HTML: https://mlsanity.com/paper/2509.07647/

## Key facts

- Cited by 14 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 34 of its 56 references that are in the map.
- First posted on arXiv 9 Sep 2025.

## 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, 30 of 34)

- [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)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Reproducible scaling laws for contrastive language-image learning](https://mlsanity.com/paper/2212.07143/) (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)
- [DiffusionDB: A Large-scale Prompt Gallery Dataset for Text-to-Image Generative Models](https://mlsanity.com/paper/2210.14896/) (2022)
- [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)
- [Robust Invisible Video Watermarking with Attention](https://mlsanity.com/paper/1909.01285/) (2019)
- [Gaussian Shading: Provable Performance-Lossless Image Watermarking for Diffusion Models](https://mlsanity.com/paper/2404.04956/) (2024)
- [Invisible Image Watermarks Are Provably Removable Using Generative AI](https://mlsanity.com/paper/2306.01953/) (2023)
- [EditGuard: Versatile Image Watermarking for Tamper Localization and Copyright Protection](https://mlsanity.com/paper/2312.08883/) (2023)
- [Watermarking Images in Self-Supervised Latent Spaces](https://mlsanity.com/paper/2112.09581/) (2021)
- [RingID: Rethinking Tree-Ring Watermarking for Enhanced Multi-Key Identification](https://mlsanity.com/paper/2404.14055/) (2024)
- [Distortion Agnostic Deep Watermarking](https://mlsanity.com/paper/2001.04580/) (2020)
- [ReDMark: Framework for Residual Diffusion Watermarking on Deep Networks](https://mlsanity.com/paper/1810.07248/) (2018)
- [RoSteALS: Robust Steganography using Autoencoder Latent Space](https://mlsanity.com/paper/2304.03400/) (2023)
- [AquaLoRA: Toward White-box Protection for Customized Stable Diffusion Models via Watermark LoRA](https://mlsanity.com/paper/2405.11135/) (2024)
- [DiffusionShield: A Watermark for Copyright Protection against Generative Diffusion Models](https://mlsanity.com/paper/2306.04642/) (2023)
- [Attack-Resilient Image Watermarking Using Stable Diffusion](https://mlsanity.com/paper/2401.04247/) (2024)
- [WMAdapter: Adding WaterMark Control to Latent Diffusion Models](https://mlsanity.com/paper/2406.08337/) (2024)
- [LaWa: Using Latent Space for In-Generation Image Watermarking](https://mlsanity.com/paper/2408.05868/) (2024)

## Built on by (most cited first, 14 of 14)

- [SHIFT: Stochastic Hidden-Trajectory Deflection for Removing Diffusion-based Watermark](https://mlsanity.com/paper/2603.29742/) (2026)
- [RAVEN: Erasing Invisible Watermarks via Novel View Synthesis](https://mlsanity.com/paper/2601.08832/) (2026)
- [OSI: One-step Inversion Excels in Extracting Diffusion Watermarks](https://mlsanity.com/paper/2602.09494/) (2026)
- [Low-Compute Watermark Removal via Dual-Domain Natural Projection](https://mlsanity.com/paper/2510.07538/) (2025)
- [TokenPure: Watermark Removal through Tokenized Appearance and Structural Guidance](https://mlsanity.com/paper/2512.01314/) (2025)
- [PhaseMark: A Post-hoc, Optimization-Free Watermarking of AI-generated Images in the Latent Frequency Domain](https://mlsanity.com/paper/2601.13128/) (2026)
- [Rethinking Forgery Attacks on Semantic Watermarks in Black-Box Settings: A Geometric Distortion Perspective](https://mlsanity.com/paper/2606.29807/) (2026)
- [Luminark: Training-free, Probabilistically-Certified Watermarking for General Vision Generative Models](https://mlsanity.com/paper/2601.01085/) (2026)
- [MarkCleaner: High-Fidelity Watermark Removal via Imperceptible Micro-Geometric Perturbation](https://mlsanity.com/paper/2602.01513/) (2026)
- [ALIEN: Analytic Latent Watermarking for Controllable Generation](https://mlsanity.com/paper/2602.06101/) (2026)
- [BiSLW: Bi-Spectral Latent Watermarking for Generative Diffusion Models](https://mlsanity.com/paper/2607.02643/) (2026)
- [Correlation-Aware and Gaussianity-Preserving Robust Latent Angular Watermarking for Diffusion Models](https://mlsanity.com/paper/2607.22386/) (2026)
- [DeepFreqMark: End-To-End Learnable Frequency-Domain Watermarking with Spherical Attack Simulation for Latent Diffusion Models](https://mlsanity.com/paper/2608.08999/) (2026)
- [Residual Transferability in Neural Image Watermarking](https://mlsanity.com/paper/2609.32241/) (2026)

## Abstract (arXiv)

Semantic watermarking techniques for latent diffusion models (LDMs) are robust against regeneration attacks, but often suffer from detection performance degradation due to the loss of frequency integrity. To tackle this problem, we propose a novel embedding method called Hermitian Symmetric Fourier Watermarking (SFW), which maintains frequency integrity by enforcing Hermitian symmetry. Additionally, we introduce a center-aware embedding strategy that reduces the vulnerability of semantic watermarking due to cropping attacks by ensuring robust information retention. To validate our approach, we apply these techniques to existing semantic watermarking schemes, enhancing their frequency-domain structures for better robustness and retrieval accuracy. Extensive experiments demonstrate that our methods achieve state-of-the-art verification and identification performance, surpassing previous approaches across various attack scenarios. Ablation studies confirm the impact of SFW on detection capabilities, the effectiveness of the center-aware embedding against cropping, and how message capacity influences identification accuracy. Notably, our method achieves the highest detection accuracy while maintaining superior image fidelity, as evidenced by FID and CLIP scores. Conclusively, our proposed SFW is shown to be an effective framework for balancing robustness and image fidelity, addressing the inherent trade-offs in semantic watermarking. Code available at https://github.com/thomas11809/SFWMark