We propose a generative multivariate posterior sampler via flow matching. It offers a simple training objective, and does not require access to likelihood evaluation. The method learns a dynamic, block-triangular velocity field in the joint space of data and parameters, which results in a deterministic transport map from a source distribution to the desired posterior. The inverse map, named vector rank, is accessible by reversibly integrating the velocity over time. It is advantageous to leverage the dynamic design: proper constraints on the velocity yield a monotone map, which leads to a conditional Brenier map, enabling a fast and simultaneous generation of Bayesian credible sets whose contours correspond to level sets of Monge-Kantorovich data depth. Our approach is computationally lighter compared to GAN-based and diffusion-based counterparts, and is capable of capturing complex posterior structures. Finally, frequentist theoretical guarantee on the consistency of the recovered posterior distribution, and of the corresponding Bayesian credible sets, is provided.

翻译：我们提出一种基于流匹配的生成式多元后验采样器。该方法提供了简单的训练目标，且无需进行似然函数评估。该方法在数据与参数的联合空间中学习动态的分块三角速度场，从而形成从源分布到目标后验分布的确定性传输映射。通过可逆地沿时间积分速度场，可获得其逆映射（称为向量秩）。动态设计的优势在于：对速度场施加适当约束可产生单调映射，进而得到条件Brenier映射，从而能够快速同步生成贝叶斯可信集——其等高线对应于Monge-Kantorovich数据深度的水平集。与基于GAN和基于扩散的方法相比，我们的方法计算量更轻，且能够捕捉复杂的后验结构。最后，我们为恢复的后验分布及相应贝叶斯可信集提供了一致性的频率学派理论保证。