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.

翻译：摘要：无导贝叶斯反演出现在科学与工程应用中，尤其是当正演模型计算成本高昂或难以进行微分时。现有无导方法在处理高维非线性问题时，会将后验分布坍缩为点估计，或返回过度自信的不确定性。我们提出的Blade方法通过相互作用粒子集合生成精确且校准良好的后验分布。Blade将扩散模型作为数据驱动先验，仅通过正演评估（即无需导数）查询正演模型。理论上，我们证明了Blade在正演模型近似误差与先验得分估计误差条件下的收敛性与稳定性。实验表明，在非线性流体动力学场景中，Blade生成的校准后验样本优于现有无导方法——该结论可通过连续秩概率评分（CRPS）、散布-技能比与秩直方图验证。其精度与校准性能随迭代次数与粒子数量持续提升，这得益于我们的收敛性与稳定性分析及实证实验的支持。