Finite-Sample Guarantees for Fully Discrete Conditional Diffusion Models
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 β>0, a suitable grid yields averaged conditional Kullback--Leibler (KL) divergence Õp(n−2β/(dx+dy+2β)) relative to the original target with or without early stopping. Both the full and early-stopped samplers attain average target total-variation (TV) error Õp(n−β/(dx+dy+2β)). Here n is the sample size, dx,dy 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.
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BibTeX
@misc{zhu2026finitesample,
title = {{Finite-Sample Guarantees for Fully Discrete Conditional Diffusion Models}},
author = {Qiuyun Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13851},
eprint = {2610.13851},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13851},
}
RIS
TY - UNPB
TI - Finite-Sample Guarantees for Fully Discrete Conditional Diffusion Models
AU - Qiuyun Zhu
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13851
UR - https://arxiv.org/abs/2610.13851
AB - 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 β>0, a suitable grid yields averaged conditional Kullback--Leibler (KL) divergence Õ_p(n^−2β/(d_x+d_y+2β)) relative to the original target with or without early stopping. Both the full and early-stopped samplers attain average target total-variation (TV) error Õ_p(n^−β/(d_x+d_y+2β)). 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.
ER -