  Sampling topological quantities in the Monte Carlo simulation of Lattice
Gauge Theory becomes challenging as we approach the continuum limit of the
theory. In this work, we introduce a Conditional Normalizing Flow (C-NF) model
to sample U(1) gauge theory in two dimensions, aiming to mitigate the impact of
topological freezing when dealing with smaller values of the U(1) bare
coupling. To train the conditional flow model, we utilize samples generated by
Hybrid Monte Carlo (HMC) method, ensuring that the autocorrelation in
topological quantities remains low. Subsequently, we employ the trained model
to interpolate the coupling parameter to values where training was not
performed. We thoroughly examine the quality of the model in this region and
generate uncorrelated samples, significantly reducing the occurrence of
topological freezing. Furthermore, we propose a re-trainable approach that
utilizes the model's own samples to enhance the generalization capability of
the conditional model. This method enables sampling for coupling values that
are far beyond the initial training region, expanding the applicability of the
model.
