Determine whether curvature dominates the ELBO gap

Determine whether the input-loss curvature term dominates the evidence lower bound gap at a data point, thereby establishing whether curvature is the leading contribution to the counterfactual sampling-time memorization quantity.

Background

The paper derives bounds connecting counterfactual memorization—defined through the change in log-likelihood when a training example is removed—to the input curvature of the corresponding leave-one-out diffusion model. This connection relies on decomposing the log-likelihood difference into a training-loss difference and an ELBO self-consistency gap.

The authors identify an unresolved issue concerning the relative size of these terms. Specifically, it is not established whether the curvature contribution is larger than, or otherwise dominates, the ELBO gap at the queried data point; resolving this comparison would determine whether curvature genuinely provides the leading-order explanation for sampling-time memorization.