  Reconstructing astrophysical and cosmological fields from observations is
challenging. It requires accounting for non-linear transformations, mixing of
spatial structure, and noise. In contrast, forward simulators that map fields
to observations are readily available for many applications. We present a
versatile Bayesian field reconstruction algorithm rooted in simulation-based
inference and enhanced by autoregressive modeling. The proposed technique is
applicable to generic (non-differentiable) forward simulators and allows
sampling from the posterior for the underlying field. We show first promising
results on a proof-of-concept application: the recovery of cosmological initial
conditions from late-time density fields.
