  Atmospheric retrievals (AR) characterize exoplanets by estimating atmospheric
parameters from observed light spectra, typically by framing the task as a
Bayesian inference problem. However, traditional approaches such as nested
sampling are computationally expensive, thus sparking an interest in solutions
based on machine learning (ML). In this ongoing work, we first explore flow
matching posterior estimation (FMPE) as a new ML-based method for AR and find
that, in our case, it is more accurate than neural posterior estimation (NPE),
but less accurate than nested sampling. We then combine both FMPE and NPE with
importance sampling, in which case both methods outperform nested sampling in
terms of accuracy and simulation efficiency. Going forward, our analysis
suggests that simulation-based inference with likelihood-based importance
sampling provides a framework for accurate and efficient AR that may become a
valuable tool not only for the analysis of observational data from existing
telescopes, but also for the development of new missions and instruments.
