An unfolding method based on conditional Invertible Neural Networks (cINN) using iterative training

1- Novel use of the conditional Invertible Neural Networks (cINN) method, which is well-regarded in other disciplines.
2- Well written, well presented.

1- The paper showcases the cINN method primarily through simple, low-dimensional examples. More examples would be helpful.
2- There is a gap in the paper, as there is no comparative study against contemporary unfolding methods, making it challenging to ascertain its advantages.

The study first introduces the collider data unfolding problem, as well as the prevalent methodologies used to tackle it, underscoring their limitations. The second section proceeds to redefine the problem through Bayesian framework. Within this framework, the manuscript introduces the cINN unfolding algorithm and the iterative approach involving training-unfolding-reweighting. The authors then put their method to the test in two distinct scenarios. The initial test (third section) involves a simplistic 1D toy model utilizing a Gaussian distribution. The subsequent scenario revolves around a more complex pp->Z\gamma\gamma process.

In summary, while the manuscript presents a novel approach to unfolding detector data, certain areas could be refined to provide a more comprehensive and clearer picture of the methodology's potential and comparative advantages.

Here are some minor feedbacks, which would be good to addressed but not necessary.

1- Very few typos: a ... flow which have, reweigthing. Some minor British/American difference in word usage.
2- I would give ref to ADAM.
3- Figure (6) is hard to follow. To enhance clarity, adopting a 3-color scheme would be recommended. This would allow readers to distinguish between positive and negative correlations.
4- Section 4 parameter space truncates at a relatively low energy level. The manuscript could benefit from elaborating on training time/complexity for extended parameter spaces.
5- The concluding remarks of the manuscript seem rather concise. Expanding this section could provide a clearer picture of the manuscript's impacts. Specifically, it would be insightful to:
5.1- Dive into the potential of the method when applied to processes with higher dimensions, i.e. more complicated processes beyond two jets.
5.2- Pit the cINN approach against other methods. If a direct comparison isn't feasible, providing quantitative evidence highlighting its superior efficiency would be beneficial, e.g. quantifying the reduction in variance, how much bias is reduced in distribution.