FPGP: Increasing Robustness of Flow-Based Watermarking to Unknown Noise Through Feature Preservation and Gradient Perturbation

Robust blind watermarking enables the accurate recovery of embedded watermarking without requiring access to the original images or message, and is widely applied in copyright protection and traceability tracking. However, existing flow-based robust blind watermarking methods typically rely on auxiliary variables during the extraction process that are inconsistent with the property of the information lost during embedding, and are often tailored to a single known noise type, resulting in limited robustness against unknown noise. To address these limitations, we propose a flow-based watermarking method that enhances robustness to unknown noise through feature preservation and gradient perturbation. Specifically, we propose a feature preservation network that learns auxiliary variables from noisy images, aligning them with the property of the lost information to improve the robustness of watermarking extraction. In addition, we design an unknown noise image generation method based on gradient perturbation, which iteratively adds perturbations to encoded images to simulate a variety of potential noise patterns that lead to watermarking extraction errors, thereby improving the robustness of watermarking against unknown noises. Experimental results validate the effectiveness of our method, demonstrating an improvement in watermarking extraction accuracy and a 10 dB increase in peak signal-to-noise ratio (from 33.5 dB to 43.8 dB). The source code is publicly available at https://github.com/reliarui/FPGP.