Hellinger-kernel conjecture for trained diffusion-model NTKs

Let $\Theta$ be the neural tangent kernel of a diffusion model and let $k_H$ denote the Hellinger kernel of its data distribution. A Hellinger kernel is understood here as the unique kernel whose geometry respects sufficient statistics. Hellinger-kernel conjecture. The NTK of a trained diffusion model converges to the Hellinger kernel $k_H$ of the data distribution—the unique kernel whose geometry respects sufficient statistics. If true, this would connect trained diffusion-model kernel geometry with information-geometric invariance; the source provides no proof or resolution evidence for the convergence claim.