Identifying Generative Path Effects in AI-Generated Image Detectors

AI generated image detectors seek statistical evidence left by modern image synthesis systems. A final image can pass through a codec (i.e., an encode–decode reconstruction stage), conditioning mechanism, and a sequence of generation updates before evaluation. However, these operations may move the same score in distinct or opposing directions, so an endpoint comparison identifies only their combined effect. To this end, we construct source-matched interventions in which each image appears as a source, after a generator codec round trip, and after ordered levels of source-conditioned image-to-image generation strength, which we term doses. Potential outcomes define codec, incremental path, dose, conditional content, and cross-generator effects for any fixed detector. Complete source crossing identifies every finite linear contrast of the intervention cell means. With an arbitrary observed coordinate set, a contrast is identified exactly when its coefficient vector lies in the row space of the coordinate projection. Consequently, the source cell, every codec cell, and every generation dose cell jointly recover all codec and incremental components, requiring 21 cell means in our four generator setting. Removing codec coordinates creates one aliasing dimension per affected generator, while constructive examples establish further ambiguity for unmatched source populations and unobserved mediators. Bounded scores and independent source sampling yield simultaneous finite sample intervals; the same estimators are exact for a frozen roster. Finally, we instantiate the theory with 58 public detectors, four versioned generators, four doses, and 2,048 sources. All 3,132 primary contrasts are identified, revealing path sensitivity, generator heterogeneity, and causal component cancellation. In addition, a text to image comparison examines the same detector profiles on complete synthesis routes.