  In radio astronomy, the challenge of reconstructing a sky map from time
ordered data (TOD) is known as an inverse problem. Standard map-making
techniques and gridding algorithms are commonly employed to address this
problem, each offering its own benefits such as producing minimum-variance
maps. However, these approaches also carry limitations such as computational
inefficiency and numerical instability in map-making and the inability to
remove beam effects in grid-based methods. To overcome these challenges, this
study proposes a novel solution through the use of the conditional invertible
neural network (cINN) for efficient sky map reconstruction. With the aid of
forward modeling, where the simulated TODs are generated from a given sky model
with a specific observation, the trained neural network can produce accurate
reconstructed sky maps. Using the five-hundred-meter aperture spherical radio
telescope (FAST) as an example, cINN demonstrates remarkable performance in map
reconstruction from simulated TODs, achieving a mean squared error of $2.29\pm
2.14 \times 10^{-4}~\rm K^2$, a structural similarity index of $0.968\pm0.002$,
and a peak signal-to-noise ratio of $26.13\pm5.22$ at the $1\sigma$ level.
Furthermore, by sampling in the latent space of cINN, the reconstruction errors
for each pixel can be accurately quantified.
