Advances in image generation have made synthetic images increasingly difficult to distinguish from real photographs, raising concerns about the trustworthiness of visual media. Existing AI-generated image detectors often perform well on in-domain data, but their robustness and cross-generator generalization remain limited. These limitations are commonly attributed to overfitting to shortcut cues. Although many methods seek to suppress shortcut learning, most retain binary classification as the training task without reconsidering how the task itself shapes the learned representations. We introduce CuRe, a framework for learning Continuous Source Responses that revisits authenticity detection from the perspective of the training task. CuRe reformulates backbone adaptation as regression of real-generated mixing ratios, providing finer supervision that encourages the model to capture authenticity-related variation beyond binary endpoint separation. We further select a compact source-response subspace to suppress nuisance variation and limit the final classifier's access to potential shortcut cues. Across ten public benchmarks, CuRe achieves an average balanced accuracy of 89.7%, exceeding the second-best method by 5.2 percentage points. Further experiments demonstrate consistent generalization gains across visual backbones and strong robustness to common image degradations. Code is available at https://github.com/manic-cui/CuRe

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