Common-Witness Certificates and Sharp Feature Bounds for Counterfactual Image Auditing

Closed yes/no spatial benchmarks can reward a correct answer even when the image adds little support beyond no-image contexts. Under a fixed forced-choice interface, Visual Credit Audit (VCA) separates two estimands: whether the benchmark image gives the model's declared decision more support than text-only and blank controls, and whether the model responds to relation-specific visual evidence. The first audit is training- and label-free and does not require an answer flip. Applying labels yields dependence-credited correctness (D-CC); on correct items, it equals same-control gold-aligned positive gain, while prediction alignment extends the audit to errors. Across four open MLLMs and two spatial benchmarks, 12.73-26.25% of decisions are correct yet uncredited. Matched same-split image permutation reduces D-CC by 21.25-47.80 points, with every paired 95% interval above zero. Fixed-pixel relation contrasts and a 3x3 evidence-source factorial show why null controls cannot identify relation response. Among controlled correct-but-uncredited agreement decisions, response to relation reversal spans 81.57-100.00%, while 32.11% pooled change answer. Independently audited outcomes on 108 geometry-compatible edits provide a bounded natural-image correspondence check. VCA thereby decomposes benchmark success into correctness, additional image support, and relation-consistent response.

Although some existing image manipulation localization (IML) methods incorporate authenticity-related supervision, this information is typically utilized merely as an auxiliary training signal to enhance the model's sensitivity to manipulation artifacts, rather than being explicitly modeled as localization evidence opposing the manipulated regions. Consequently, when manipulation traces are subtle or degraded by post-processing and noise, these methods struggle to explicitly compare manipulated and authentic evidence, resulting in unreliable predictions in ambiguous areas. To address these issues, we propose a courtroom-style adjudication framework that regards IML task as the confrontation of evidence followed by judgment. The framework comprises a prosecution stream, a defense stream, and a judge model. We first build a dual-hypothesis segmentation architecture on a shared multi-scale encoder, in which the prosecution stream asserts manipulation and the defense stream asserts authenticity. Guided by edge priors, it produces evidence for manipulated and authentic regions through cascaded multi-level fusion, bidirectional disagreement suppression, and dynamic debate refinement. We further develop a reinforcement learning judge model that performs strategic re-inference and refinement on uncertain regions, yielding a manipulated-region mask. The judge model is trained with advantage-based rewards and a soft-IoU objective, and reliability is calibrated via entropy and cross-hypothesis consistency. Experimental results show that our model achieves superior average performance compared with SOTA IML methods.

Two-sample testing is a fundamental tool for detecting distributional differences across scientific domains, but classical tests (including kernel-based tests) can be ineffective on high-dimensional structured data such as images. Recent deep two-sample tests improve sensitivity in these settings by learning informative representations, yet they provide limited insight into which data features drive rejection of the null hypothesis $H_0$. To address this issue, we propose a counterfactual explanation framework for deep two-sample testing that generates sample-level edits moving observations from a source group toward a target group while explicitly reducing the discrepancy measured by the test. Our method combines a diffusion autoencoder with a pretrained deep two-sample test model and optimizes a maximum mean discrepancy (MMD) objective in the test model's representation space to produce plausible counterfactuals. We quantify distribution-level effects through changes in the test statistic and the resulting two-sample p-values. We evaluate the method on synthetic 2D shape datasets and two MRI cohorts. Across both settings, the counterfactual transformations consistently increase p-values relative to the original samples, indicating that the edited source set becomes statistically closer to the target distribution under the test. We measure minimality using LPIPS to ensure the counterfactuals remain close to the original samples. The resulting edits provide interpretable evidence of the features associated with the detected group differences. On MRI, the localized changes are consistent with known anatomical differences between cohorts.