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Deep learning-based digital watermarking frameworks have been widely studied recently. Most existing methods adopt an ``encoder-noise layer-decoder''-based architecture where the embedding and extraction processes are accomplished separately by the encoder and the decoder. However, one potential drawback of such a framework is that the encoder and the decoder may not be well coupled, resulting in the fact that the encoder may embed some redundant features into the host image thus influencing the invisibility and robustness of the whole algorithm. To address this limitation, this paper proposes a flow-based robust watermarking framework. The basic component of such framework is an invertible up-down-sampling neural block that can realize the embedding and extraction simultaneously. As a consequence, the encoded feature could keep high consistency with the feature that the decoder needed, which effectively avoids the embedding of redundant features. In addition, to ensure the robustness of black-box distortion, an invertible noise layer (INL) is designed to simulate the distortion and is served as a noise layer in the training stage. Benefiting from its reversibility, INL is also applied as a preprocessing before extraction to eliminate the distortion, which further improves the robustness of the algorithm. Extensive experiments demonstrate the superiority of the proposed framework in terms of visual quality and robustness. Compared with the state-of-the-art architecture, the visual quality (measured by PSNR) of the proposed framework improves by 2dB and the extraction accuracy after JPEG compression (QF=50) improves by more than 4%. Besides, the robustness against black-box distortions can be greatly achieved with more than 95% extraction accuracy.