扩散模型让复杂模拟中的参数推断更可靠，尤其适合数据不完整或有误差的情况。
A Review of Diffusion-based Simulation-Based Inference: Foundations and Applications in Non-Ideal Data Scenarios
- 用扩散模型直接学习后验分布，无需计算似然函数
- 在模型不匹配、数据缺失等现实问题下仍保持推断准确
- 适合做地质物理等科学计算中的不确定性量化
对于复杂的模拟问题，由于似然函数难以计算，传统基于似然的方法通常不可行。模拟基推断（SBI）提供了一种无需似然的替代方法，可直接从模拟器输出中学习后验分布 $p(ftheta mid fxobs)$。近期，扩散模型成为SBI的有力工具，克服了早期神经似然/后验估计与归一化流方法的局限。本文从基础原理出发，系统回顾扩散模型在非理想数据场景下的应用，重点关注科学计算中常见的三类挑战：模型误设（模拟器与真实世界不一致）、无结构或无穷维观测数据、以及数据缺失。我们整合数学基础，综述八种应对策略，如针对不规则数据的条件扩散、用于先验适配的引导扩散、提升效率的序列与因子化方法，以及支持快速采样的一致性模型。全文保持符号一致，并强调获得准确后验所需的条件。最后，讨论开放性问题及在地球物理不确定性量化中的应用前景。
原文摘要 · Abstract (English)
For complex simulation problems, inferring parameters often precludes the use of classical likelihood-based techniques due to intractable likelihoods. Simulation-based inference (SBI) methods offer a likelihood-free approach to directly learn posterior distributions $p(\bftheta \mid \xobs)$ from simulator outputs. Recently, diffusion models have emerged as promising tools for SBI, addressing limitations of earlier neural methods such as neural likelihood/posterior estimation and normalizing flows. This review examines diffusion-based SBI from first principles to applications, emphasizing robustness in three non-ideal data scenarios common to scientific computing: model misspecification (simulator-reality mismatch), unstructured or infinite-dimensional observations, and missing data. We synthesize mathematical foundations and survey eight methods addressing these challenges, such as conditional diffusion for irregular data, guided diffusion for prior adaptation, sequential and factorized approaches for efficiency, and consistency models for fast sampling. Throughout, we maintain consistent notation and emphasize conditions required for accurate posteriors. We conclude with open problems and applications to geophysical uncertainty quantification, where these challenges are acute.
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