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Luminark: Training-free, Probabilistically-Certified Watermarking for General Vision Generative Models

Jiayi Xu, Zhang Zhang, Yuanrui Zhang, Ruitao Chen, Yixian Xu, Tianyu He, Di He

TL;DR

Luminark introduces a training-free, probabilistically-certified watermarking framework for general vision generative models by embedding a patch-level luminance signature defined via a random binary pattern and thresholds. Detection is performed through a statistically grounded match-rate test with calibrated false positive control, while watermark injection leverages a plug-and-play Watermark Guidance that steers generation toward the signature without sacrificing image quality. The approach is demonstrated across diffusion, autoregressive, and hybrid models, achieving strong detection reliability (>95% under various transformations) and near-reference generation fidelity (FID close to unwatermarked baselines). By combining principled luminance-based signatures with model-agnostic guidance, Luminark offers a scalable, general-purpose watermarking solution with practical privacy and misuse-prevention implications.

Abstract

In this paper, we introduce \emph{Luminark}, a training-free and probabilistically-certified watermarking method for general vision generative models. Our approach is built upon a novel watermark definition that leverages patch-level luminance statistics. Specifically, the service provider predefines a binary pattern together with corresponding patch-level thresholds. To detect a watermark in a given image, we evaluate whether the luminance of each patch surpasses its threshold and then verify whether the resulting binary pattern aligns with the target one. A simple statistical analysis demonstrates that the false positive rate of the proposed method can be effectively controlled, thereby ensuring certified detection. To enable seamless watermark injection across different paradigms, we leverage the widely adopted guidance technique as a plug-and-play mechanism and develop the \emph{watermark guidance}. This design enables Luminark to achieve generality across state-of-the-art generative models without compromising image quality. Empirically, we evaluate our approach on nine models spanning diffusion, autoregressive, and hybrid frameworks. Across all evaluations, Luminark consistently demonstrates high detection accuracy, strong robustness against common image transformations, and good performance on visual quality.

Luminark: Training-free, Probabilistically-Certified Watermarking for General Vision Generative Models

TL;DR

Luminark introduces a training-free, probabilistically-certified watermarking framework for general vision generative models by embedding a patch-level luminance signature defined via a random binary pattern and thresholds. Detection is performed through a statistically grounded match-rate test with calibrated false positive control, while watermark injection leverages a plug-and-play Watermark Guidance that steers generation toward the signature without sacrificing image quality. The approach is demonstrated across diffusion, autoregressive, and hybrid models, achieving strong detection reliability (>95% under various transformations) and near-reference generation fidelity (FID close to unwatermarked baselines). By combining principled luminance-based signatures with model-agnostic guidance, Luminark offers a scalable, general-purpose watermarking solution with practical privacy and misuse-prevention implications.

Abstract

In this paper, we introduce \emph{Luminark}, a training-free and probabilistically-certified watermarking method for general vision generative models. Our approach is built upon a novel watermark definition that leverages patch-level luminance statistics. Specifically, the service provider predefines a binary pattern together with corresponding patch-level thresholds. To detect a watermark in a given image, we evaluate whether the luminance of each patch surpasses its threshold and then verify whether the resulting binary pattern aligns with the target one. A simple statistical analysis demonstrates that the false positive rate of the proposed method can be effectively controlled, thereby ensuring certified detection. To enable seamless watermark injection across different paradigms, we leverage the widely adopted guidance technique as a plug-and-play mechanism and develop the \emph{watermark guidance}. This design enables Luminark to achieve generality across state-of-the-art generative models without compromising image quality. Empirically, we evaluate our approach on nine models spanning diffusion, autoregressive, and hybrid frameworks. Across all evaluations, Luminark consistently demonstrates high detection accuracy, strong robustness against common image transformations, and good performance on visual quality.
Paper Structure (22 sections, 1 theorem, 9 equations, 20 figures, 4 tables, 6 algorithms)

This paper contains 22 sections, 1 theorem, 9 equations, 20 figures, 4 tables, 6 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Watermarking as Luminance Constraints
  4. Watermark Definition
  5. Probabilistically-Certified Watermark Detection
  6. Watermark Injection via Step-wise Guidance
  7. Experiment
  8. Robustness
  9. Fidelity
  10. Ablation Study
  11. Conclusions, Limitations, and Future Directions
  12. Proof of Proposition 1
  13. Implementation of Image Transformations for Robust Detection
  14. Visualization of the Watermarked Images
  15. Guided Sampling for Latent Diffusion Models
  16. ...and 7 more sections

Key Result

Proposition 1

Assume each $c_i$ is drawn i.i.d from $\operatorname{Bernoulli}(\frac{1}{2})$ with support $\{-1,1\}$ and each $\tau_i$ is drawn i.i.d from any distribution with support $(0,1)$, then for any fixed $\mathbf{x}$, for any $0 \leq \varepsilon \leq \frac{1}{2}$, we have where $D_{KL}(\varepsilon)=(\frac{1}{2}+\varepsilon)\ln(1+2\varepsilon)+(\frac{1}{2}-\varepsilon)\ln(1-2\varepsilon)$ and $\lceil y

Figures (20)

  • Figure 1: Luminark on $\text{Stable Diffusion 2.1}$. Left: unwatermarked output. Right: watermarked output.
  • Figure 2: Illustration of Luminark. The watermark is defined as a patch-wise binary pattern (visualized by '+'/'-' symbols) over the luminance values, i.e., whether the luminance exceeds the threshold (visualized by the grayscale intensity). Generation is performed by injecting the pattern using guidance. Detection is performed by comparing the pattern in the image and the predefined pattern.
  • Figure 3: Visualization of Stable-Diffusion Version2.1: Prompt (left): The Gates of Valhalla, grand and imposing, with Valkyries flying around, Norse mythology, epic, divine lighting, matte painting, masterpiece. Prompt (mid): A cheerful anime girl with vibrant pink hair and large expressive eyes, wearing a school uniform, cherry blossoms falling, digital art, by Makoto Shinkai. Prompt (right): A stoic Roman centurion in full armor, standing guard, detailed armor and helmet, realistic, historical, cinematic shot.
  • Figure 4: Visualization of Stable-Diffusion Version2.1 Prompt (left): A field of glowing lavender under the Milky Way, astrophotography, stunning, magical, long exposure. Prompt (mid): A quaint, cobblestone alleyway in a European village, colorful houses with flower boxes, charming, sunny day.Prompt (right): A luxurious Art Deco hotel lobby, geometric patterns, gold and black color scheme, elegant, 1920s style.
  • Figure 5: Visualization of Stable-Diffusion Version2.1: Prompt (left): An infinity pool on a rooftop overlooking a modern city skyline at dusk, luxurious, serene, beautiful view. Prompt (mid): The interior of a futuristic spaceship bridge, holographic displays, panoramic view of space, clean design, sci-fi. Prompt (right): An ancient, ruined Greek temple on a cliffside, overlooking the Aegean Sea, historical, majestic, golden hour.
  • ...and 15 more figures

Theorems & Definitions (2)

  • Proposition 1
  • proof