Neural posterior estimation methods based on dis-crete normalizing flows have become establishedtools for simulation-based inference (SBI), butscaling them to high-dimensional problems can bechallenging. Building on recent advances in gen-erative modeling, we here present flow matchingposterior estimation (FMPE), a technique for SBIusing continuous normalizing flows. Like diffu-sion models, and in contrast to discrete flows, flowmatching allows for unconstrained architectures,providing enhanced flexibility for complex datamodalities. Flow matching, therefore, enablesexact density evaluation, fast training, and seam-less scalability to large architectures—making itideal for SBI. To showcase the improved scalabil-ity of our approach, we apply it to a challengingastrophysics problem: for gravitational-wave in-ference, FMPE outperforms methods based oncomparable discrete flows, reducing training timeby 30% with substantially improved accuracy