# Normalizing Flows to Reconstruct Pseudo-PDFs

arXiv: https://arxiv.org/abs/2607.25282 · HTML: https://mlsanity.com/paper/2607.25282/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 17 references that are in the map.
- First posted on arXiv 28 Jul 2026.

## Builds on (most cited first, 6 of 6)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [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)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Machine Learning of Linear Differential Equations using Gaussian Processes](https://mlsanity.com/paper/1701.02440/) (2017)
- [Quantization Of Probability Measures In Maximum~Mean~Discrepancy Distance](https://mlsanity.com/paper/2503.11868/) (2025)

## Abstract (arXiv)

We investigate a normalizing-flow approach for reconstructing parton distribution functions (PDFs) from synthetic matrix-element data. Our framework combines Gaussian Process priors with invertible neural networks to learn a posterior distribution over PDFs consistent with limited Ioffe-time data. We demonstrate that the architecture preserves physical constraints and extrapolation properties.