Finite-Sample Guarantees for Fully Discrete Conditional Diffusion Models

arXiv:2610.13851v1 Announce Type: cross Abstract: We establish finite-sample guarantees for conditional diffusion models learned from data and implemented with finitely many denoising steps. Our approach aligns the score-training objective with the sampling grid, allowing statistical estimation and numerical discretization errors to be analyzed together. Under a smooth conditional density model, we derive high-probability bounds on the generated distribution's error and quantify the required number of score evaluations. For every smoothness index eta>0, a suitable grid yields averaged conditional Kullback--Leibler (KL) divergence widetilde O_p(n^{-2eta/(d_x+d_y+2eta)}) relative to the original target with or without early stopping. Both the full and early-stopped samplers attain average target total-variation (TV) error widetilde O_p(n^{-eta/(d_x+d_y+2eta)}). Here n is the sample size, d_x,d_y are the data and conditioning dimensions, and errors are averaged over the conditioning variable. The total-variation bound matches the rate established in existing conditional distribution-estimation theory, up to logarithmic factors.

Source: arXiv cs.LG | 2026-10-12