用简单理论统一解释多种扩散模型，让生成更直观可靠。
Random Walks with Tweedie: A Unified View of Score-Based Diffusion Models
- 基于随机游走与特威迪分布，推导出通用生成框架
- 多个主流扩散模型可归为该框架下的特定参数选择
- 支持条件采样且无需近似似然，适合信号处理研究者
我们提出一种简洁的推导方法，仅依赖少数基础课本结论，统一解释若干重要的基于得分的扩散模型。扩散模型近年来成为生成真实合成信号（尤其是自然图像）的强大工具，并在图像处理中的反问题算法中占据重要地位。尽管这些算法往往出人意料地简单，其理论基础却十分复杂，文献中存在多种复杂的理论解释。本文为信号处理领域提供了一种简单且基本自洽的理论依据，可生成通用的训练与采样算法模板。我们证明多个有影响力的扩散模型对应于该模板中的特定选择，并表明其他更直接的算法选择也能获得相当的结果。该方法还具备无需似然近似的条件采样优势。
原文摘要 · Abstract (English)
We present a concise derivation for several influential score-based diffusion models that relies on only a few textbook results. Diffusion models have recently emerged as powerful tools for generating realistic, synthetic signals -- particularly natural images -- and often play a role in state-of-the-art algorithms for inverse problems in image processing. While these algorithms are often surprisingly simple, the theory behind them is not, and multiple complex theoretical justifications exist in the literature. Here, we provide a simple and largely self-contained theoretical justification for score-based diffusion models that is targeted towards the signal processing community. This approach leads to generic algorithmic templates for training and generating samples with diffusion models. We show that several influential diffusion models correspond to particular choices within these templates and demonstrate that alternative, more straightforward algorithmic choices can provide comparable results. This approach has the added benefit of enabling conditional sampling without any likelihood approximation.
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