Preprint
Finite-Sample Guarantees for Fully Discrete Conditional Diffusion Models
arXiv
arXiv
10/09/2026
DOI: 10.48550/arxiv.2610.13851
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 indexβ>0 , a suitable grid yields averaged conditional Kullback–Leibler (KL) divergence\widetilde O_(p)(n^(-2β/(dₓ+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\widetilde O_(p)(n^(-β/(dₓ+d_(y)+2β))) . Herenis the sample size,dₓ,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.
Details
- Title: Subtitle
- Finite-Sample Guarantees for Fully Discrete Conditional Diffusion Models
- Creators
- Qiuyun Zhu - University of Iowa
- Resource Type
- Preprint
- Publication Details
- arXiv
- DOI
- 10.48550/arxiv.2610.13851
- ISSN
- 2331-8422
- Publisher
- arXiv
- Language
- English
- Date posted
- 10/09/2026
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9985244643902771
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