提出新型生成模型的理论保证，适用于重尾数据。
Non-asymptotic Analysis of Diffusion Annealed Langevin Monte Carlo for Generative Modelling
- 用扩散路径与朗之万蒙特卡洛结合，构建新生成框架
- 首次给出重尾分布下生成模型的非渐近误差界
- 适合关注生成模型理论基础的研究者
本文研究在弱数据分布假设下，一般扩散（插值）路径及其朗之万蒙特卡洛实现的理论性质，称为扩散退火朗之万蒙特卡洛（DALMC）。我们分析并给出了退火朗之万动力学的非渐近误差界，其中分布路径定义为数据分布的高斯卷积，如扩散模型所示。随后将结果扩展至近期提出的重尾（学生t分布）扩散路径，首次为重尾数据分布提供了理论保证。该分析为一类在有限时间内从简单分布（高斯或学生t）插值到数据分布的基于得分的生成模型提供了理论支持。相比传统基于前向奥恩斯坦-乌伦贝克（OU）噪声过程的方法，此方法具有更广的适用视角。
原文摘要 · Abstract (English)
We investigate the theoretical properties of general diffusion (interpolation) paths and their Langevin Monte Carlo implementation, referred to as diffusion annealed Langevin Monte Carlo (DALMC), under weak conditions on the data distribution. Specifically, we analyse and provide non-asymptotic error bounds for the annealed Langevin dynamics where the path of distributions is defined as Gaussian convolutions of the data distribution as in diffusion models. We then extend our results to recently proposed heavy-tailed (Student's t) diffusion paths, demonstrating their theoretical properties for heavy-tailed data distributions for the first time. Our analysis provides theoretical guarantees for a class of score-based generative models that interpolate between a simple distribution (Gaussian or Student's t) and the data distribution in finite time. This approach offers a broader perspective compared to standard score-based diffusion approaches, which are typically based on a forward Ornstein-Uhlenbeck (OU) noising process.
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