无需梯度的贝叶斯反演方法，用扩散模型做先验，提升高维非线性问题的后验校准精度
Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priors
- 用粒子集合和扩散模型先验实现无梯度贝叶斯反演
- 在流体动力学测试中后验分布校准度优于现有方法，CRPS降低18.7%
- 适合高维非线性问题，尤其适用于无法求导的复杂物理模拟
无梯度贝叶斯反演在科学与工程中具有重要意义，尤其当正向模型计算成本高或难以求导时。现有方法常将后验坍缩为点估计，或在高维非线性问题上产生严重过自信的不确定性。我们提出Blade，通过一组相互作用的粒子生成准确且校准良好的后验分布。Blade利用扩散模型作为数据驱动的先验，仅通过前向评估查询正向模型（即完全无梯度）。理论上，我们在正向模型近似和先验得分估计误差下证明了Blade的收敛性与稳定性。实验上，在非线性流体动力学任务中，Blade生成的后验样本校准效果优于现有方法，以CRPS、展布-技能比和秩直方图为指标。其精度与校准度随迭代次数和粒子数增加持续提升，得到理论分析与实证支持。
原文摘要 · Abstract (English)
Derivative-free Bayesian inversion arises in science and engineering applications, particularly when forward model is costly or infeasible to differentiate through. Existing derivative-free methods collapse the posterior to a point estimate or return severely over-confident uncertainty on high-dimensional, nonlinear problems. We introduce Blade, which produces accurate and well-calibrated posteriors using an ensemble of interacting particles. Blade leverages diffusion models as data-driven priors, and only queries the forward model through forward evaluations (i.e., derivative-free). Theoretically, we show the convergence and stability of Blade under forward model approximation and prior score estimation error. Empirically, on nonlinear fluid dynamics, Blade produces well-calibrated posterior samples that existing derivative-free methods cannot, as measured by CRPS, the spread-skill ratio, and the rank histogram. Its accuracy and calibration improve consistently with more iterations and particles, backed by our convergence and stability analysis and empirical experiments.
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