Finite-Sample Guarantees for Fully Discrete Conditional Diffusion Models
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 $\widetilde O_p(n^{-2β/(d_x+d_y+2β)})$ relative to the original target with or without early stopping. Both t...
| Authors | Qiuyun Zhu |
|---|---|
| Primary category | stat.ML |
| Published | 9 October 2026 |
| Last updated at source | 9 October 2026 |
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