# Generative Unfolding with Distribution Mapping

arXiv: https://arxiv.org/abs/2411.02495 · HTML: https://mlsanity.com/paper/2411.02495/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 73 references that are in the map.
- First posted on arXiv 4 Nov 2024.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (2023)
- [Lorentz-Equivariant Geometric Algebra Transformers for High-Energy Physics](https://mlsanity.com/paper/2405.14806/) (2024)
- [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)
- [A Lorentz-Equivariant Transformer for All of the LHC](https://mlsanity.com/paper/2411.00446/) (2024)
- [DCTRGAN: Improving the Precision of Generative Models with Reweighting](https://mlsanity.com/paper/2009.03796/) (2020)
- [End-To-End Latent Variational Diffusion Models for Inverse Problems in High Energy Physics](https://mlsanity.com/paper/2305.10399/) (2023)
- [Neural Empirical Bayes: Source Distribution Estimation and its Applications to Simulation-Based Inference](https://mlsanity.com/paper/2011.05836/) (2020)
- [Generative Networks for Precision Enthusiasts](https://mlsanity.com/paper/2110.13632/) (2021)
- [An unfolding method based on conditional Invertible Neural Networks (cINN) using iterative training](https://mlsanity.com/paper/2212.08674/) (2022)
- [The Landscape of Unfolding with Machine Learning](https://mlsanity.com/paper/2404.18807/) (2024)
- [Understanding Event-Generation Networks via Uncertainties](https://mlsanity.com/paper/2104.04543/) (2021)
- [EPiC-ly Fast Particle Cloud Generation with Flow-Matching and Diffusion](https://mlsanity.com/paper/2310.00049/) (2023)
- [Improving Generative Model-based Unfolding with Schr"odinger Bridges](https://mlsanity.com/paper/2308.12351/) (2023)
- [Scaffolding Simulations with Deep Learning for High-dimensional Deconvolution](https://mlsanity.com/paper/2105.04448/) (2021)
- [Full Event Particle-Level Unfolding with Variable-Length Latent Variational Diffusion](https://mlsanity.com/paper/2404.14332/) (2024)
- [Flow Matching Beyond Kinematics: Generating Jets with Particle-ID and Trajectory Displacement Information](https://mlsanity.com/paper/2312.00123/) (2023)

## Built on by (most cited first, 6 of 6)

- [Simulation-Prior Independent Neural Unfolding Procedure](https://mlsanity.com/paper/2507.15084/) (2025)
- [Profiling systematic uncertainties in Simulation-Based Inference with Factorizable Normalizing Flows](https://mlsanity.com/paper/2602.13184/) (2026)
- [Generative Models and Statistical Validation](https://mlsanity.com/paper/2605.30453/) (2026)
- [Factorizable Normalizing Flows for parameter-dependent density morphing](https://mlsanity.com/paper/2606.30489/) (2026)
- [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)

## Abstract (arXiv)

Machine learning enables unbinned, highly-differential cross section measurements. A recent idea uses generative models to morph a starting simulation into the unfolded data. We show how to extend two morphing techniques, Schr"odinger Bridges and Direct Diffusion, in order to ensure that the models learn the correct conditional probabilities. This brings distribution mapping to a similar level of accuracy as the state-of-the-art conditional generative unfolding methods. Numerical results are presented with a standard benchmark dataset of single jet substructure as well as for a new dataset describing a 22-dimensional phase space of Z + 2-jets.