Where Does the Watermark Hide? Push-Pull Disentanglement for Invisible Watermark Removal

arXiv:2609.31722v1 Announce Type: new Abstract: Fixed image distortions do not cover an attacker that learns from paired clean and watermarked images. We study this paired-training threat with single-image inference: deployment uses neither the clean reference nor the watermark key, payload, or decoder. An encoder maps each image to a structural latent $g$ and an auxiliary residual latent $u$. Push supervision reconstructs the watermarked image from $D(g_w,u_w)$. Pull supervision trains the zero-auxiliary output $D(A_g(g_w;k),0)$ toward the paired clean image. At $k=1.10,u=0$, the four-method sweep gives an average BER of $0.3958$, PSNR of $31.07$ dB, and SSIM of $0.9554$. Restoring $u$ from $0$ to $0.15$ moves average BER from $0.3893$ to $0.3357$, while PSNR falls from $30.99$ to $28.23$ dB. The intervention supports decoder dependence on the auxiliary input in the evaluated setting. The accompanying theory is a conditional, post-hoc account of this behavior rather than an experimentally verified information-relocation result.