Synthetic Image Detection via Spectral Gaps of QC-RBIM Nishimori Bethe-Hessian Operators

Abstract: The rapid advance of deep generative models such as GANs and diffusion networks now produces images that are virtually indistinguishable from genuine photographs, undermining media forensics and biometric security. Supervised detectors quickly lose effectiveness on unseen generators or after adversarial post-processing, while existing unsupervised methods that rely on low-level statistical cues remain fragile. We introduce a physics-inspired, model-agnostic detector that treats synthetic-image identification as a community-detection problem on a sparse weighted graph. Image features are first extracted with pretrained CNNs and reduced to 32 dimensions, each feature vector becomes a node of a Multi-Edge Type QC-LDPC graph. Pairwise similarities are transformed into edge couplings calibrated at the Nishimori temperature, producing a Random Bond Ising Model (RBIM) whose Bethe-Hessian spectrum exhibits a characteristic gap when genuine community structure (real images) is present. Synthetic images violate the Nishimori symmetry and therefore lack such gaps. We validate the approach on binary tasks cat versus dog and male versus female using real photos from Flickr-Faces-HQ and CelebA and synthetic counterparts generated by GANs and diffusion models. Without any labeled synthetic data or retraining of the feature extractor, the detector achieves over 94% accuracy. Spectral analysis shows multiple well separated gaps for real image sets and a collapsed spectrum for generated ones. Our contributions are threefold: a novel LDPC graph construction that embeds deep image features, an analytical link between Nishimori temperature RBIM and the Bethe-Hessian spectrum providing a Bayes optimal detection criterion; and a practical, unsupervised synthetic image detector robust to new generative architectures. Future work will extend the framework to video streams and multi-class anomaly detection.