The Null Is the Hard Part: Exact Tests for Memorization in Generative Models

Sushovan Majhi, Pramita Bagchi

Memorization audits of generative models read similarity scores against thresholds, with no null distribution, and the conclusions they support can be wrong. By MemBench's rule, the benchmark's mitigations roughly halve Stable Diffusion's memorization; audited with false-discovery control, two thirds of the certified images are no longer detected under random prompt perturbations, five sixths under attention rescaling, and all of them under embedding optimization. The field's data-copying test, read against its own null, flags ten of twenty-four generators that reproduce nothing. We argue that for memorization the null is the hard part, and supply two. For a whole model, training and held-out images are exchangeable given its samples, and relabelling them is a permutation test, exact for any statistic when the held-out images are a random split; under it, a nearest-neighbour preference still fires on seven of those twenty-four, and a count restricted to the near-duplicate scale on none (McNemar p=0.016). For single images, the natural nulls fail twice, measurably: ranking an image among random images yields 596 false discoveries among 2,365 controls, and resampling independent…