The rise of generative Artificial Intelligence (AI) has made detecting AI-generated images a critical challenge for ensuring authenticity. Existing reconstruction-based methods lack theoretical foundations and on empirical heuristics, limiting interpretability and reliability. In this paper, we introduce the Jacobian-Spectral Lower Bound for reconstruction error from a geometric perspective, showing that real images off the reconstruction manifold exhibit a non-trivial error lower bound, while generated images on the manifold have near-zero error. Furthermore, we reveal the limitations of existing methods that rely on static reconstruction error from a single pass. These methods often fail when some real images exhibit lower error than generated ones. This counterintuitive behavior reduces detection accuracy and requires data-specific threshold tuning, limiting their applicability in real-world scenarios. To address these challenges, we propose ReGap, a training-free method that computes dynamic reconstruction error by leveraging structured editing operations to introduce controlled perturbations. This enables measuring error changes before and after editing, improving detection accuracy by enhancing error separation. Experimental results show that our method outperforms existing baselines, exhibits robustness to common post-processing operations and generalizes effectively across diverse conditions.

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