提出抗异常值的扩散后验采样方法，提升贝叶斯反问题求解鲁棒性。
Outlier-robust Diffusion Posterior Sampling for Bayesian Inverse Problems
- 基于梯度的扩散后验采样，引入异常值鲁棒性设计。
- 在含异常值的线性和非线性任务中均实现稳定性能提升。
- 兼容现有采样器，适用于科学计算与自然图像反问题。
扩散模型已成为贝叶斯反问题（BIPs）中强有力的先验学习工具。基于扩散的求解器依赖于观测数据的预设似然函数来引导生成过程。实际应用中似然函数误设常见，尤其在异常值污染下会显著降低恢复性能。本文首先刻画了由此引起的后验偏差，并证明了线性BIPs中扩散求解器的稳定性。分析进一步揭示现有扩散求解器在异常值污染下的潜在鲁棒性缺陷。为此，我们提出一种简单而有效的方法：鲁棒扩散后验采样，该方法在线性BIPs上具有可证明的抗异常值能力，且与现有基于梯度的后验采样器兼容。在科学反问题和自然图像任务上的实证结果表明，该方法在含异常值的挑战性场景中持续提升性能，适用于线性和非线性任务。
原文摘要 · Abstract (English)
Diffusion models have emerged as powerful learned priors for Bayesian inverse problems (BIPs). Diffusion-based solvers rely on a presumed likelihood for the observations in BIPs to guide the generation process. Likelihood misspecification is common in practical BIPs and is known to degrade recovery performance, particularly under outlier contamination. We investigate this problem by first characterizing the induced posterior deviation and proving the stability of diffusion-based solvers for linear BIPs. Our stability analysis further reveals potential robustness deficiencies of existing diffusion-based solvers under outlier-contaminated measurements. To address this issue, we propose a simple yet effective solution: robust diffusion posterior sampling, which is provably outlier-robust for linear BIPs and compatible with existing gradient-based posterior samplers. Empirical results from scientific inverse problems and natural image tasks demonstrate the effectiveness and robustness of our method, with consistent performance gains in challenging scenarios involving outlier contamination for both linear and nonlinear tasks.
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