CheckMate! Watermarking Graph Diffusion Models in Polynomial Time

Watermarking provides an effective means for data governance. However, conventional post-editing graph watermarking approaches degrade the graph quality and involve NP-hard subroutines. Alternatively, recent approaches advocate for embedding watermarking patterns in the noisy latent during data generation from diffusion models, but remain uncharted for graph models due to the hardness of inverting the graph diffusion process. In this work, we propose CheckWate: the first watermarking framework for graph diffusion models embedding checkerboard watermark and providing polynomial time verification. To address NP-completeness due to graph isomorphism, CheckWate embeds the watermark into the latent eigenvalues, which are isomorphism-invariant. To detect the watermark through reversing the graph diffusion process, CheckWate leverages the graph eigenvectors to approximately dequantize the discrete graph back to the continuous latent, with theoretical guarantees on the detectability and dequantization error. We further introduce a latent sparsification mechanism to enhance the robustness of CheckWate against graph modifications. We evaluate CheckWate on four datasets and four graph modification attacks, against three generation time watermark schemes. CheckWate achieves remarkable generation quality while being detectable under strong attacks such as isomorphism, whereas the baselines are unable to detect the watermark. Code available at: https://github.com/r-gheda/checkwate.