Conditional Flow Matching for Bayesian Posterior Inference

About

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.

Percy S. Zhai, So Won Jeong, Veronika Ročková · 2025

Related benchmarks

Task	Dataset	Result
Simulation-Based Inference	SBIBM Gaussian Linear	C2ST0.71	19
Simulation-Based Inference	Gaussian Linear	Computation Time (s)0.01	8
Simulation-Based Inference	Gaussian Mixture	Computation Time (s)0.01	8
Simulation-Based Inference	Bernoulli GLM	Computation Time (s)0.01	8
Simulation-Based Inference	Two Moons	Computation Time (s)0.01	8
Simulation-Based Inference	SLCP	Inference Time (s)0.01	8
Posterior Sampling	Bernoulli GLM SBI	C2ST92	7
Posterior Sampling	Gaussian Mixture SBI benchmark	C2ST82	7
Posterior Sampling	SLCP SBI benchmark	C2ST93	7
Posterior Sampling	Two Moons SBI benchmark	C2ST74	6