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

arXiv: https://arxiv.org/abs/2212.08674 · HTML: https://mlsanity.com/paper/2212.08674/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 52 references that are in the map.
- First posted on arXiv 16 Dec 2022.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [Cubic-Spline Flows](https://mlsanity.com/paper/1906.02145/) (2019)
- [OmniFold: A Method to Simultaneously Unfold All Observables](https://mlsanity.com/paper/1911.09107/) (2019)
- [How to GAN away Detector Effects](https://mlsanity.com/paper/1912.00477/) (2019)
- [Generative Networks for Precision Enthusiasts](https://mlsanity.com/paper/2110.13632/) (2021)

## Built on by (most cited first, 20 of 20)

- [A Lorentz-Equivariant Transformer for All of the LHC](https://mlsanity.com/paper/2411.00446/) (2024)
- [End-To-End Latent Variational Diffusion Models for Inverse Problems in High Energy Physics](https://mlsanity.com/paper/2305.10399/) (2023)
- [The Landscape of Unfolding with Machine Learning](https://mlsanity.com/paper/2404.18807/) (2024)
- [nu2-Flows: Fast and improved neutrino reconstruction in multi-neutrino final states with conditional normalizing flows](https://mlsanity.com/paper/2307.02405/) (2023)
- [Full Event Particle-Level Unfolding with Variable-Length Latent Variational Diffusion](https://mlsanity.com/paper/2404.14332/) (2024)
- [Calorimeter shower superresolution](https://mlsanity.com/paper/2308.11700/) (2023)
- [Unifying Simulation and Inference with Normalizing Flows](https://mlsanity.com/paper/2404.18992/) (2024)
- [Generative Unfolding with Distribution Mapping](https://mlsanity.com/paper/2411.02495/) (2024)
- [Scaling laws for amplitude surrogates](https://mlsanity.com/paper/2601.13308/) (2026)
- [Unbinned Profiled Unfolding](https://mlsanity.com/paper/2302.05390/) (2023)
- [Comparison of Affine and Rational Quadratic Spline Coupling and Autoregressive Flows through Robust Statistical Tests](https://mlsanity.com/paper/2302.12024/) (2023)
- [Simulation-Prior Independent Neural Unfolding Procedure](https://mlsanity.com/paper/2507.15084/) (2025)
- [BUFF: Boosted Decision Tree based Ultra-Fast Flow matching](https://mlsanity.com/paper/2404.18219/) (2024)
- [Extrapolating Jet Radiation with Autoregressive Transformers](https://mlsanity.com/paper/2412.12074/) (2024)
- [An Introduction to Bayesian and Frequentist Simulation-Based Inference with Machine Learning](https://mlsanity.com/paper/2607.21702/) (2026)
- [Unknown Unknowns: Model Misspecification in Machine Learning for Physics](https://mlsanity.com/paper/2608.13633/) (2026)
- [Designing Observables for Measurements with Deep Learning](https://mlsanity.com/paper/2310.08717/) (2023)
- [Machine Learning-based Unfolding for Cross Section Measurements in the Presence of Nuisance Parameters](https://mlsanity.com/paper/2512.07074/) (2025)
- [Inverse Problems Conditioned on Observation Ensembles: Applications and Methods](https://mlsanity.com/paper/2601.22029/) (2026)
- [ScatterPrism: convergence for generative simulation and inverse problems in particle and nuclear physics](https://mlsanity.com/paper/2604.01313/) (2026)

## Abstract (arXiv)

The unfolding of detector effects is crucial for the comparison of data to theory predictions. While traditional methods are limited to representing the data in a low number of dimensions, machine learning has enabled new unfolding techniques while retaining the full dimensionality. Generative networks like invertible neural networks~(INN) enable a probabilistic unfolding, which map individual events to their corresponding unfolded probability distribution. The accuracy of such methods is however limited by how well simulated training samples model the actual data that is unfolded. We introduce the iterative conditional INN~(IcINN) for unfolding that adjusts for deviations between simulated training samples and data. The IcINN unfolding is first validated on toy data and then applied to pseudo-data for the pp → Z γ γ process.