The authors describe proper distributional learning in diffusion models as learning to reverse a diffusion process over the underlying data density. A failure mode called memorization occurs when the reverse process instead learns diffusion tied to individual training samples.

They derive an analytical characterization of such memorized reverse processes. They then propose a detection criterion that flags the thermodynamic singularity the authors associate with this form of memorization.

When tested on a range of neural network models designed to promote or reduce memorization, the proposed criterion reliably distinguished properly learned networks from memorizing ones.

This provides a diagnostic supported by the analytical characterization and the reported tests across multiple model designs. The brief does not report numerical performance details or broader limitations beyond the evaluated conditions.