  Neural posterior estimation methods based on discrete normalizing flows have
become established tools for simulation-based inference (SBI), but scaling them
to high-dimensional problems can be challenging. Building on recent advances in
generative modeling, we here present flow matching posterior estimation (FMPE),
a technique for SBI using continuous normalizing flows. Like diffusion models,
and in contrast to discrete flows, flow matching allows for unconstrained
architectures, providing enhanced flexibility for complex data modalities. Flow
matching, therefore, enables exact density evaluation, fast training, and
seamless scalability to large architectures--making it ideal for SBI. We show
that FMPE achieves competitive performance on an established SBI benchmark, and
then demonstrate its improved scalability on a challenging scientific problem:
for gravitational-wave inference, FMPE outperforms methods based on comparable
discrete flows, reducing training time by 30% with substantially improved
accuracy. Our work underscores the potential of FMPE to enhance performance in
challenging inference scenarios, thereby paving the way for more advanced
applications to scientific problems.
