FoRM: Preserving First-Order Real-Manifold Geometry for Generalizable AI-Generated Image Detection

As generative models continue to evolve rapidly, generalization to unseen generators has become a central challenge in generalizable AI-generated image detection. Recent reconstruction-based, real-centric envelope learning methods construct near-real fake samples to characterize the outer boundary of the real manifold, offering a promising approach to cross-generator generalization. However, these methods do not sufficiently guarantee a key prerequisite of envelope learning—the stability of the real manifold enclosed by the envelope. Once the real manifold becomes distorted during training, even a well-characterized outer boundary cannot compensate for the resulting discriminative bias caused by the degradation of its internal structure. To address this limitation, we propose FoRM, a first-order real-manifold preservation framework. Specifically, FoRM performs pointwise feature anchoring against a frozen visual foundation model to establish zeroth-order consistency in real representations. Nevertheless, pointwise consistency alone is insufficient to determine the local shape and geometric directions of sample neighborhoods. We therefore introduce Local Directional Jacobian Alignment (LJ), which matches the local responses and their magnitudes between the teacher and detector along natural image variation directions. LJ extends pointwise consistency to local first-order geometric consistency, thereby mitigating local geometric contraction and distortion of the real manifold. Furthermore, FoRM introduces distributionally diverse real samples to prevent real-side optimization from persistently concentrating on homogeneous local regions, enhancing the structural stability of the real manifold from a data-centric perspective. It also employs heterogeneous reconstruction mechanisms to construct diverse near-real fake samples to strengthen outer-boundary supervision. By jointly modeling the internal geometry of the real manifold and its surrounding discriminative envelope, FoRM achieves competitive cross-generator generalization performance across 12 benchmarks.