Finite-Sample Guarantees for Fully Discrete Conditional Diffusion Models
Paper proves finite-sample error bounds for conditional diffusion models using finite denoising steps.
The paper proves finite-sample guarantees for conditional diffusion models trained from data and run with finitely many denoising steps. Aligning the score objective with the sampling grid yields high-probability bounds: averaged conditional KL divergence scales as Õ_p(n^{-2β/(d_x+d_y+2β)}) and total variation as Õ_p(n^{-β/(d_x+d_y+2β)}), with or without early stopping. The total-variation rate matches existing conditional distribution-estimation theory up to logarithmic factors.
- Score training is aligned with the finite sampling grid
- KL and total-variation bounds cover estimation and discretization
- Rates hold with and without early stopping
- TV rate matches prior conditional estimation theory up to logs
From the original article
1 min read at arxiv.orgWe 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.
By Qiuyun Zhu · arxiv.org
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