Blind watermarking provides powerful evidence for copyright protection, image authentication, and tampering identification. However, it remains a challenge to design a watermarking model with high imperceptibility and robustness against strong noise attacks. To resolve this issue, we present a framework Combining the Invertible and Non-invertible (CIN) mechanisms. The CIN is composed of the invertible part to achieve high imperceptibility and the non-invertible part to strengthen the robustness against strong noise attacks. For the invertible part, we develop a diffusion and extraction module (DEM) and a fusion and split module (FSM) to embed and extract watermarks symmetrically in an invertible way. For the non-invertible part, we introduce a non-invertible attention-based module (NIAM) and the noise-specific selection module (NSM) to solve the asymmetric extraction under a strong noise attack. Extensive experiments demonstrate that our framework outperforms the current state-of-the-art methods of imperceptibility and robustness significantly. Our framework can achieve an average of 99.99% accuracy and 67.66 dB PSNR under noise-free conditions, while 96.64% and 39.28 dB combined strong noise attacks. The code will be available in https://github.com/rmpku/CIN.
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