基准测试 扩散 化 基于 贝叶斯式 逆向 问题解决者
Evan Scope Crafts1, Umberto Villa1,2
1Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712 USA.
IEEE open journal of signal processing
|September 25, 2025
概括
本研究介绍了基准问题和一个框架 (BIPSDA) 来评估贝叶斯反向问题的扩散模型样本. 这允许在生成式建模应用中严格评估不确定性量化.
科学领域:
- 计算数学 计算数学 计算数学
- 机器学习 机器学习
- 图像处理 图像处理
背景情况:
- 扩散模型是最先进的生成模型,越来越多地被用作贝叶斯反向问题的先验.
- 扩散模型与后端采样概率函数的最佳整合仍然是一个公开的挑战.
- 由于未知的分析先验,当前的评估方法在严格的不确定性量化中扎.
研究的目的:
- 引入分析已知的后台的基准问题,用于评估基于扩散模型的样本.
- 提出一个一般的框架,贝叶斯反向问题解决者通过扩散化 (BIPSDA),用于基于扩散模型的后端采样.
- 为了使基于扩散模型的贝叶斯推理中不确定性量化的原则性评估.
主要方法:
- 开发了三个基准问题,灵感来自图像绘制,X射线断层扫描和相位检索.
- 通过扩散化 (BIPSDA) 框架引入了贝叶斯反向问题解决者,统一了现有的和新的算法.
- 测试了BIPSDA算法与基准问题对比,以评估性能和不确定性量化.
主要成果:
- 基准问题允许近似的基准真相后面采样用于绩效评估.
- BIPSDA框架整合了各种基于扩散的后端采样方法.
- 评估提供了关于当前基于扩散模型的后部样本的优点和局限性的见解.
结论:
- 提出的基准问题为未来开发基于扩散模型的采样提供了一个标准化的平台.
- 该BIPSDA框架有助于开发和评估贝叶斯反向问题的新算法.
- 这项工作推进了对不确定性量化的严格评估,用于逆向问题的生成模型.
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