提出统一分析框架，破解扩散模型确定性采样收敛难题。
Unified Convergence Analysis for Score-Based Diffusion Models with Deterministic Samplers
- 构建通用分析框架，适用于多种前向过程与确定性采样器。
- 对VP过程+指数积分器，实现˜O(d²/ε)迭代复杂度。
- 首次系统分析DDIM类采样器，获多项式复杂度保障。
基于分数的扩散模型已成为从高维数据分布生成样本的强大工具，其过程分为两步：先通过加噪将数据分布转化为已知先验分布，再通过采样从噪声中恢复原始分布。在各类采样方法中，确定性采样器因效率更高而备受关注，但其分析面临独特挑战——传统方法如Girsanov定理仅适用于随机采样器，难以适用。此外，现有研究多聚焦具体实例，缺乏对一般前向过程和多样化确定性采样器的通用分析。本文提出统一收敛性分析框架，以验证其有效性：针对方差保持（VP）前向过程与指数积分器（EI）方案，获得˜O(d²/ε)的迭代复杂度；同时对尚未充分研究的去噪扩散隐式模型（DDIM）类采样器进行详尽分析，实现多项式迭代复杂度。
原文摘要 · Abstract (English)
Score-based diffusion models have emerged as powerful techniques for generating samples from high-dimensional data distributions. These models involve a two-phase process: first, injecting noise to transform the data distribution into a known prior distribution, and second, sampling to recover the original data distribution from noise. Among the various sampling methods, deterministic samplers stand out for their enhanced efficiency. However, analyzing these deterministic samplers presents unique challenges, as they preclude the use of established techniques such as Girsanov's theorem, which are only applicable to stochastic samplers. Furthermore, existing analysis for deterministic samplers usually focuses on specific examples, lacking a generalized approach for general forward processes and various deterministic samplers. Our paper addresses these limitations by introducing a unified convergence analysis framework. To demonstrate the power of our framework, we analyze the variance-preserving (VP) forward process with the exponential integrator (EI) scheme, achieving iteration complexity of $\tilde O(d^2/ε)$. Additionally, we provide a detailed analysis of Denoising Diffusion Implicit Models (DDIM)-type samplers, which have been underexplored in previous research, achieving polynomial iteration complexity.
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