# Profiling systematic uncertainties in Simulation-Based Inference with Factorizable Normalizing Flows

arXiv: https://arxiv.org/abs/2602.13184 · HTML: https://mlsanity.com/paper/2602.13184/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 39 references that are in the map.
- First posted on arXiv 13 Feb 2026.

## Builds on (most cited first, 16 of 16)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transport](https://mlsanity.com/paper/2006.00104/) (2020)
- [Convex Potential Flows: Universal Probability Distributions with Optimal Transport and Convex Optimization](https://mlsanity.com/paper/2012.05942/) (2020)
- [A Guide to Constraining Effective Field Theories with Machine Learning](https://mlsanity.com/paper/1805.00020/) (2018)
- [Neural Networks for Full Phase-space Reweighting and Parameter Tuning](https://mlsanity.com/paper/1907.08209/) (2019)
- [Generative Unfolding with Distribution Mapping](https://mlsanity.com/paper/2411.02495/) (2024)
- [One flow to correct them all: improving simulations in high-energy physics with a single normalising flow and a switch](https://mlsanity.com/paper/2403.18582/) (2024)
- [Simulation-Prior Independent Neural Unfolding Procedure](https://mlsanity.com/paper/2507.15084/) (2025)
- [Data-Driven High-Dimensional Statistical Inference with Generative Models](https://mlsanity.com/paper/2506.06438/) (2025)

## Built on by (most cited first, 2 of 2)

- [Recovering Weak Signals with Normalizing Flows](https://mlsanity.com/paper/2609.06382/) (2026)
- [Machine learning for the LHC physics program: a 2025-2026 stocktake](https://mlsanity.com/paper/2609.32874/) (2026)

## Abstract (arXiv)

Unbinned likelihood fits maximize the information extracted from experimental data, yet their application in realistic high-dimensional analyses has been fundamentally bottlenecked by the prohibitive computational cost of profiling systematic uncertainties. Furthermore, current machine learning-based inference methods typically estimate scalar parameters, discarding complex high-dimensional correlations. To address this, we propose a general Simulation-Based Inference (SBI) framework that elevates the fit target from scalar parameters to a multivariate Distribution of Interest (DoI), a learnable, invertible transformation of the feature space. We employ Factorizable Normalizing Flows to model systematic variations as parametric deformations, preserving tractability without combinatorial explosion. Crucially, we develop an amortized training strategy that learns the conditional dependence of the DoI on nuisance parameters in a single optimization process, bypassing repetitive training during likelihood scans. To capture the finite-sample statistical variance of the neural network DoI, we introduce a Poisson-bootstrap ensemble, which we marginalize through an averaged likelihood to deliver a complete statistical-plus-systematic uncertainty budget within a single unbinned likelihood. Validated on a synthetic dataset emulating a high-energy physics measurement, our method demonstrates that rigorous, fully profiled unbinned measurements can now be extended to complete differential distributions. By turning the fit into a functional measurement, this approach offers a powerful, unifying framework for a broad range of tasks conventionally treated as distinct problems, from detector calibration and differential cross-sections to unfolding and continuous parameter estimation.