首次给出离散扩散模型的样本复杂度理论分析，证明其高效训练可行性。
Discrete State Diffusion Models: A Sample Complexity Perspective
- 通过分解得分估计误差为统计、近似、优化与截断四部分，建立理论框架
- 首次获得 $ ilde{ m O}(ε^{-2})$ 的样本复杂度上界，量化训练需求
- 为文本、序列等离散任务的扩散模型提供理论支撑，适合研究者参考
扩散模型在视觉、语言及科学领域生成高维数据方面表现卓越。尽管连续状态扩散模型已得到广泛实证与理论研究，但涉及文本、序列和组合结构的应用所依赖的离散状态扩散模型，其理论理解仍严重不足。现有分析均假设得分估计误差有界，却未探讨样本复杂度。本文提出一个系统的理论框架，首次给出离散状态扩散模型的样本复杂度上界 $ ilde{ m O}(ε^{-2})$。通过对得分估计误差进行统计、近似、优化与截断的结构化分解，揭示了高效训练的关键机制。该工作填补了文献中的根本空白，确立了离散状态扩散模型的理论可处理性与实际相关性。
原文摘要 · Abstract (English)
Diffusion models have demonstrated remarkable performance in generating high-dimensional samples across domains such as vision, language, and the sciences. Although continuous-state diffusion models have been extensively studied both empirically and theoretically, discrete-state diffusion models, essential for applications involving text, sequences, and combinatorial structures, remain significantly less understood from a theoretical standpoint. In particular, all existing analyses of discrete-state models assume score estimation error bounds without studying sample complexity results. In this work, we present a principled theoretical framework for discrete-state diffusion, providing the first sample complexity bound of $\widetilde{\mathcal{O}}(ε^{-2})$. Our structured decomposition of the score estimation error into statistical, approximation, optimization, and clipping components offers critical insights into how discrete-state models can be trained efficiently. This analysis addresses a fundamental gap in the literature and establishes the theoretical tractability and practical relevance of discrete-state diffusion models.
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