Sharp Convergence and Sampling Trade-offs for Riemannian Diffusion under Nonnegative Ricci Curvature

Diffusion models have emerged as state-of-the-art generative models, with recent extensions from Euclidean spaces to Riemannian manifolds. However, existing convergence guarantees for Riemannian diffusion models typically require $\tilde{O}(\mathrm{poly}(d,T)/ε^2)$ score evaluations, with potentiall