From Gist to Verbatim: the Controllable Path of One Image Through a Diffusion Prior

Modern generative models are typically studied for their ability to generalize, while memorization is treated as a failure mode. We invert this perspective and ask how a generative model can recall a single datum. We frame memorization as a control problem: a learned conditioning signal steers a frozen diffusion model toward a target image, and we follow the formation of this memory throughout training. Before converging to exact reproduction (*verbatim*), memory passes through a regime of *abstraction*: samples preserve the target's semantic content (*gist*) while remaining diverse in appearance, leaving predictable detail to the generative prior. This semantic organization emerges despite the absence of labels, captions, or any explicit semantic objective. In the abstraction regime, the learned memory approaches ordinary text conditioning and supports editing, one-shot recognition, and retrieval more effectively than in the near-perfect reconstruction regime. These results suggest that memorization can serve as a probe of the relevance structure encoded by a generative model: what must be stored about a datum, what can be reconstructed from prior knowledge, and how learned memories interpolate between reconstructive recall and literal data storage.