# END2: Robust Dual-Decoder Watermarking Framework Against Non-Differentiable Distortions

arXiv: https://arxiv.org/abs/2412.09960 · HTML: https://mlsanity.com/paper/2412.09960/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 26 references that are in the map.
- First posted on arXiv 13 Dec 2024.

## Built on by (most cited first, 1 of 1)

- [DVP-MVS: Synergize Depth-Edge and Visibility Prior for Multi-View Stereo](https://mlsanity.com/paper/2412.11578/) (2024)

## Abstract (arXiv)

DNN-based watermarking methods have rapidly advanced, with the ``Encoder-Noise Layer-Decoder'' (END) framework being the most widely used. To ensure end-to-end training, the noise layer in the framework must be differentiable. However, real-world distortions are often non-differentiable, leading to challenges in end-to-end training. Existing solutions only treat the distortion perturbation as additive noise, which does not fully integrate the effect of distortion in training. To better incorporate non-differentiable distortions into training, we propose a novel dual-decoder architecture (END2). Unlike conventional END architecture, our method employs two structurally identical decoders: the Teacher Decoder, processing pure watermarked images, and the Student Decoder, handling distortion-perturbed images. The gradient is backpropagated only through the Teacher Decoder branch to optimize the encoder thus bypassing the problem of non-differentiability. To ensure resistance to arbitrary distortions, we enforce alignment of the two decoders' feature representations by maximizing the cosine similarity between their intermediate vectors on a hypersphere. Extensive experiments demonstrate that our scheme outperforms state-of-the-art algorithms under various non-differentiable distortions. Moreover, even without the differentiability constraint, our method surpasses baselines with a differentiable noise layer. Our approach is effective and easily implementable across all END architectures, enhancing practicality and generalizability.