用扩散模型先验解决反问题采样难题，方法简单有效。
A Gibbs posterior sampler for inverse problem based on prior diffusion model
- 基于扩散模型构建先验，设计吉布斯采样算法解决反问题。
- 在小规模模拟实验中验证了算法有效性与收敛性。
- 适合从事贝叶斯反演、生成先验建模的研究者参考。
本文针对线性观测加噪声、问题病态且依赖贝叶斯正则化的反问题，提出一种基于扩散模型先验的吉布斯后验采样方法。该场景下后验采样长期存在困难，而本文首次探索吉布斯途径，结果表明其不仅实现简单，且效果显著。研究还提供了特定情形下的收敛性保证，并为实际应用中该性质提供支持依据。数值实验基于一个简化示例，清晰验证了方法的有效性。
原文摘要 · Abstract (English)
This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive error, (2) the problem is ill-posed and regularization relies on a Bayesian strategy, (3)~the prior is modeled by a diffusion process adjusted on an available large set of examples. In this context, it is known that the issue of posterior sampling is a thorny one and the paper introduces a Gibbs algorithm. It appears that this avenue has not been explored, and we show that it is particularly effective and remarkably simple. In addition, it provides clear elements regarding convergence guarantees in a specific case and arguments supporting such guarantees in practical cases. The results are clearly confirmed by numerical simulations based on a toy example.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。