Derivative-free Bayesian inversion is an important task in many science and engineering applications, particularly when computing the forward model derivative is computationally and practically challenging. In this paper, we introduce Blade, which can produce accurate and well-calibrated posteriors for Bayesian inversion using an ensemble of interacting particles. Blade leverages powerful data-driven priors based on diffusion models, and can handle nonlinear forward models that permit only black-box access (i.e., derivative-free). Theoretically, we establish a non-asymptotic convergence analysis to characterize the effects of forward model and prior estimation errors. Empirically, Blade achieves superior performance compared to existing derivative-free Bayesian inversion methods on various inverse problems, including challenging highly nonlinear fluid dynamics.

翻译：无导数贝叶斯反演是众多科学与工程应用中的一项重要任务，尤其当计算前向模型导数在计算和实践中面临挑战时。本文提出Blade方法，该方法通过一组相互作用的粒子集合，能够为贝叶斯反演生成准确且校准良好的后验分布。Blade利用基于扩散模型的强大数据驱动先验，并能处理仅允许黑箱访问（即无导数）的非线性前向模型。理论上，我们建立了非渐近收敛分析以刻画前向模型与先验估计误差的影响。实证表明，在包括具有挑战性的高度非线性流体动力学在内的多种反问题上，Blade相比现有无导数贝叶斯反演方法取得了更优的性能。