The Value of Covariance Matching in Gaussian DDPMs and the Lanczos Sampler

ArXi:2605.22723v1 Announce Type: cross A central error measure in Gaussian DDPMs is the path-space KL divergence between the exact reverse chain and the learned Gaussian reverse process. This quantity is especially relevant for procedures such as classifier guidance, which perturb the entire reverse trajectory rather than only the terminal sample. Prior analyses show that standard isotropic reverse covariances suffer an unavoidable $\Omega(1/T)$ path-KL error as the number of denoising steps $T$ grows.