Bayesian Inverse Problems Meet Flow Matching: Efficient and Flexible Inference via Transformers

Daniil Sherki, Ivan Oseledets, Ekaterina Muravleva

Keywords: Flow Matching, Inverse Problems, Bayesian Inverse Problems, Transformer

Abstract: In this paper, we present a new framework that combines Conditional Flow Matching (CFM) with a transformer-based architecture. This enables us to sample fast and flexibly from complex posterior distributions when solving Bayesian inverse problems. The methodology directly learns conditional probability trajectories from the data, leveraging CFM’s ability to bypass iterative simulation and transformers’ capacity to process an arbitrary number of observations. The primary outcomes show that relative parameter recovery errors are as low as 1.5\%, and that inference time is reduced by up to 2,000 times on a CPU compared to the Markov Chain Monte Carlo, as demonstrated by three Bayesian problems.

Submission Number: 26