# Flow Away your Differences: Conditional Normalizing Flows as an Improvement to Reweighting

arXiv: https://arxiv.org/abs/2304.14963 · HTML: https://mlsanity.com/paper/2304.14963/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 42 references that are in the map.
- First posted on arXiv 28 Apr 2023.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Approximating Likelihood Ratios with Calibrated Discriminative Classifiers](https://mlsanity.com/paper/1506.02169/) (2015)
- [GANplifying Event Samples](https://mlsanity.com/paper/2008.06545/) (2020)
- [Neural Networks for Full Phase-space Reweighting and Parameter Tuning](https://mlsanity.com/paper/1907.08209/) (2019)
- [Reweighting with Boosted Decision Trees](https://mlsanity.com/paper/1608.05806/) (2016)
- [Transport away your problems: Calibrating stochastic simulations with optimal transport](https://mlsanity.com/paper/2107.08648/) (2021)

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

- [EPiC-ly Fast Particle Cloud Generation with Flow-Matching and Diffusion](https://mlsanity.com/paper/2310.00049/) (2023)
- [Learning Likelihood Ratios with Neural Network Classifiers](https://mlsanity.com/paper/2305.10500/) (2023)
- [Calorimeter shower superresolution](https://mlsanity.com/paper/2308.11700/) (2023)
- [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)
- [Unknown Unknowns: Model Misspecification in Machine Learning for Physics](https://mlsanity.com/paper/2608.13633/) (2026)
- [LiD-GLM: Lipschitz-constrained Deep Generalized Linear Models](https://mlsanity.com/paper/2608.16340/) (2026)

## Abstract (arXiv)

We present an alternative to reweighting techniques for modifying distributions to account for a desired change in an underlying conditional distribution, as is often needed to correct for mis-modelling in a simulated sample. We employ conditional normalizing flows to learn the full conditional probability distribution from which we sample new events for conditional values drawn from the target distribution to produce the desired, altered distribution. In contrast to common reweighting techniques, this procedure is independent of binning choice and does not rely on an estimate of the density ratio between two distributions. In several toy examples we show that normalizing flows outperform reweighting approaches to match the distribution of the target.We demonstrate that the corrected distribution closes well with the ground truth, and a statistical uncertainty on the training dataset can be ascertained with bootstrapping. In our examples, this leads to a statistical precision up to three times greater than using reweighting techniques with identical sample sizes for the source and target distributions. We also explore an application in the context of high energy particle physics.