In radio astronomy, the challenge of reconstructing a sky map from time ordered data 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 time-ordered data (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 as an example, cINN demonstrates remarkable performance in map reconstruction from simulated TODs, achieving a mean squared error of 2.29 ± 2.14 × 10−4 K2, a structural similarity index of 0.968 ± 0.002, and a peak signal-to-noise ratio of 26.13 ± 5.22 at the 1σ level. Furthermore, by sampling in the latent space of cINN, the reconstruction errors for each pixel can be accurately quantified.