# The NFLikelihood: an unsupervised DNNLikelihood from Normalizing Flows

arXiv: https://arxiv.org/abs/2309.09743 · HTML: https://mlsanity.com/paper/2309.09743/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 33 references that are in the map.
- First posted on arXiv 18 Sep 2023.

## Builds on (most cited first, 11 of 11)

- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [A Living Review of Machine Learning for Particle Physics](https://mlsanity.com/paper/2102.02770/) (2021)
- [Continual Repeated Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2201.13117/) (2022)
- [Neural Adaptive Sequential Monte Carlo](https://mlsanity.com/paper/1506.03338/) (2015)
- [Flow-based sampling for multimodal and extended-mode distributions in lattice field theory](https://mlsanity.com/paper/2107.00734/) (2021)
- [Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics](https://mlsanity.com/paper/2309.01156/) (2023)
- [Inference Networks for Sequential Monte Carlo in Graphical Models](https://mlsanity.com/paper/1602.06701/) (2016)
- [HMC with Normalizing Flows](https://mlsanity.com/paper/2112.01586/) (2021)
- [Comparison of Affine and Rational Quadratic Spline Coupling and Autoregressive Flows through Robust Statistical Tests](https://mlsanity.com/paper/2302.12024/) (2023)

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

- [Learning to Validate Generative Models: a Goodness-of-Fit Approach](https://mlsanity.com/paper/2511.09118/) (2025)
- [Testable Likelihoods for Beyond-the-Standard Model Fits](https://mlsanity.com/paper/2309.10365/) (2023)

## Abstract (arXiv)

We propose the NFLikelihood, an unsupervised version, based on Normalizing Flows, of the DNNLikelihood proposed in Ref.[1]. We show, through realistic examples, how Autoregressive Flows, based on affine and rational quadratic spline bijectors, are able to learn complicated high-dimensional Likelihoods arising in High Energy Physics (HEP) analyses. We focus on a toy LHC analysis example already considered in the literature and on two Effective Field Theory fits of flavor and electroweak observables, whose samples have been obtained throught the HEPFit code. We discuss advantages and disadvantages of the unsupervised approach with respect to the supervised one and discuss possible interplays of the two.