Link coverage to task-level novelty and perceptual quality

Establish rigorous connections between the (α,δ,c)-coverage guarantees for diffusion-model sampling on data manifolds and task-level metrics of novelty and perceptual quality for generated samples.

Background

The paper formalizes generalization via geometric coverage of the data manifold, rather than full density recovery. However, practitioners care about novelty and perceptual quality.

The authors explicitly note that translating geometric coverage into task-level or perceptual metrics remains an unresolved problem.