Graph-level anomaly detection decides whether an entire graph deviates from the nominal data-generating process, with applications in fraud networks, molecular screening, and social systems. Existing approaches rely mainly on discriminative embeddings and heuristic scoring, limiting interpretability and robustness. We implement and extend a density-estimation formulation that learns graph likelihoods using discrete flow matching on continuous-time Markov chains defined over node and edge states. To stabilize reverse transitions and preserve permutation invariance, we introduce a Gromov-Wasserstein (GW) optimal-transport coupling in the reverse path; we also adopt Beta-distributed time sampling to concentrate steps near 0 and 1, capturing rapid regime changes. We benchmark on TU datasets and Tox21-style molecular graphs, reporting AUROC and ablations against strong baselines. We expect competitive-or state-of-the-art-performance and deliver a reproducible open-source implementation with practical guidance for graph anomaly evaluation.
