GenSymAudit: Anchor-Relative Auditing of Distributional Symmetry in Generative Models

Generative models are increasingly deployed through fixed sampling and conditioning pipelines, yet structural properties of their output distributions are often inferred from the training data or ancestor model rather than measured on the deployed artifact itself. We study this problem through distributional symmetry and introduce GenSymAudit, a sample-only framework for auditing whether a deployed generative artifact changes the element-wise symmetry profile of the real distribution it is intended to model. This problem cannot be addressed by testing generated samples against perfect symmetry: real data may already contain substantial directional structure, while the deployed distribution additionally depends on the model checkpoint, conditioning protocol, sampler, guidance, and sampling budget. GenSymAudit constructs condition-matched real and generated pools, measures transformation-specific separability using grouped classifier two-sample tests, and assigns anchor-relative verdicts using negative controls, calibrated uncertainty, multiplicity correction, and quality gates. Both fMoW and Git-10M exhibit strong departures from perfect $D_4$ invariance. Relative to these real-data anchors, DiffusionSat exhibits three statistically resolved amplifications, dominated by vertical reflection (+18.11 points), while Text2Earth shows smaller bidirectional changes, attenuating horizontal reflection (-2.98 points) and amplifying vertical reflection (+3.62 points). Controlled few-step experiments further show that likelihood-derived symmetry certificates can become numerically unreliable while independent sample-space measurements continue to detect asymmetry. These findings support the broader conclusion that structural properties should be measured on the complete artifact actually deployed rather than inferred from its reference data, ancestor model, or nominal sampling configuration.