评估扩散逆求解器生成样本与真实后验分布的匹配度,揭示准确率之外的不确定性真相。
Beyond Accuracy: Evaluating Posterior Fidelity of Diffusion Inverse Solvers
- 通过已知解析后验的仿真环境系统测试各类扩散逆求解器的后验保真度。
- 提出无需真值的score-KSD指标,可衡量生成样本分布与目标得分场的一致性。
- 发现高重建精度不等于好后验一致性,为实际问题提供更可信的不确定性诊断。
不确定性评估在科学与工程逆问题中至关重要。然而,现有扩散逆求解器(DIS)的基准主要关注重建准确性,忽视了不确定性与分布行为。由于随机逆求解器通过基于扩散的后验采样表示不确定性,评估其生成样本是否准确捕捉目标后验分布,成为不确定性量化的重要环节。为弥补这一不足并深入理解扩散采样器的分布特性,我们在已知解析真后验的受控仿真环境中,系统研究了多种现有DIS方法的后验保真度。此外,针对真实逆问题中无真后验的情况,我们提出基于得分的核斯坦差距(score-KSD),一种理论基础扎实且无需真值的度量,用于评估生成样本分布与由前向模型和学习到的扩散先验诱导的目标得分场的一致性。通过仿真实验与真实逆问题求解验证,score-KSD展现出有效性,能提供超越重建准确性的后验保真度诊断,揭示出更高重建精度并不必然对应更好的后验一致性。
原文摘要 · Abstract (English)
Uncertainty evaluation is critical in scientific and engineering inverse problems. However, existing benchmarks on Diffusion Inverse Solvers (DIS) primarily focus on reconstruction accuracy but overlook uncertainty and distributional behavior. Since stochastic inverse solvers represent uncertainty through diffusion-based posterior samples, evaluating how well their generated samples capture the target posterior distribution becomes an important aspect of uncertainty quantification. To address this limitation and better understand the distributional behavior of diffusion samplers, we conduct a systematic study to investigate the posterior fidelity of a broad range of existing DIS methods in controlled simulation settings with a known analytical true posterior. Furthermore, to enable posterior-aware evaluation on real-world inverse problems where ground-truth posterior is unavailable, we propose score-based Kernel Stein Discrepancy (score-KSD), a theoretically-grounded and ground-truth-free metric that measures the consistency of the distribution of generated samples from a DIS method with the target posterior score field, induced by the forward model and learned diffusion prior. Through both simulation experiments and real-world inverse problem solving, we validate the effectiveness of the proposed score-KSD and demonstrate that it provides meaningful posterior fidelity diagnostics beyond reconstruction accuracy, revealing that higher reconstruction accuracy does not necessarily imply better posterior consistency.
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