  In this study, we introduce a method for estimating sound fields in
reverberant environments using a conditional invertible neural network (CINN).
Sound field reconstruction can be hindered by experimental errors, limited
spatial data, model mismatches, and long inference times, leading to
potentially flawed and prolonged characterizations. Further, the complexity of
managing inherent uncertainties often escalates computational demands or is
neglected in models. Our approach seeks to balance accuracy and computational
efficiency, while incorporating uncertainty estimates to tailor reconstructions
to specific needs. By training a CINN with Monte Carlo simulations of random
wave fields, our method reduces the dependency on extensive datasets and
enables inference from sparse experimental data. The CINN proves versatile at
reconstructing Room Impulse Responses (RIRs), by acting either as a likelihood
model for maximum a posteriori estimation or as an approximate posterior
distribution through amortized Bayesian inference. Compared to traditional
Bayesian methods, the CINN achieves similar accuracy with greater efficiency
and without requiring its adaptation to distinct sound field conditions.
