提出新框架，让扩散模型无需模拟即可快速生成。
Simulation-free and finite-time diffusion model
- 设计可解析的时变条件分布，构造对应参考过程。
- 实现无模拟训练与有限时间生成的统一。
- 揭示得分匹配非本质，而是反向过程自然产物。
生成扩散模型的性能取决于连接经验分布与先验分布的参考扩散过程的选择。传统方法通常在无模拟训练与有限时间生成之间权衡。本文提出一种设计参考过程的新框架，能够同时实现二者。核心思想是预设可解析的时变条件分布，并构造以它们为边际分布的参考过程。该框架表明，得分匹配并非扩散模型训练的根本机制，而是参考过程反向推导时自然出现的结果。进一步证明，条件流匹配是该框架在小噪声极限下的特例。
原文摘要 · Abstract (English)
The performance of generative diffusion models is determined by the choice of the reference diffusion process connecting the empirical and prior distributions. Conventional approaches typically trade off simulation-free training against finite-time generation. We propose a framework for designing the reference process that achieves both simultaneously. The key idea is to prescribe tractable time-dependent conditional distributions and then construct the reference process realizing them as its marginals. This framework reveals that score matching is not fundamental to diffusion-model training but instead emerges naturally through reversal of the reference process. We further show that conditional flow matching arises as the small-noise limit of the proposed framework.
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