# Unifying Simulation and Inference with Normalizing Flows

arXiv: https://arxiv.org/abs/2404.18992 · HTML: https://mlsanity.com/paper/2404.18992/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 123 references that are in the map.
- First posted on arXiv 29 Apr 2024.

## Builds on (most cited first, 30 of 37)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [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)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [CaloGAN: Simulating 3D High Energy Particle Showers in Multi-Layer Electromagnetic Calorimeters with Generative Adversarial Networks](https://mlsanity.com/paper/1712.10321/) (2017)
- [Anomaly Detection with Density Estimation](https://mlsanity.com/paper/2001.04990/) (2020)
- [Accelerating Science with Generative Adversarial Networks: An Application to 3D Particle Showers in Multi-Layer Calorimeters](https://mlsanity.com/paper/1705.02355/) (2017)
- [CaloFlow: Fast and Accurate Generation of Calorimeter Showers with Normalizing Flows](https://mlsanity.com/paper/2106.05285/) (2021)
- [CaloFlow II: Even Faster and Still Accurate Generation of Calorimeter Showers with Normalizing Flows](https://mlsanity.com/paper/2110.11377/) (2021)
- [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)
- [i-flow: High-dimensional Integration and Sampling with Normalizing Flows](https://mlsanity.com/paper/2001.05486/) (2020)
- [Neural Density Estimation and Likelihood-free Inference](https://mlsanity.com/paper/1910.13233/) (2019)
- [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)
- [Understanding Event-Generation Networks via Uncertainties](https://mlsanity.com/paper/2104.04543/) (2021)
- [CaloFlow for CaloChallenge Dataset 1](https://mlsanity.com/paper/2210.14245/) (2022)
- [Improving Generative Model-based Unfolding with Schr"odinger Bridges](https://mlsanity.com/paper/2308.12351/) (2023)
- [High-dimensional and Permutation Invariant Anomaly Detection](https://mlsanity.com/paper/2306.03933/) (2023)
- [nu-Flows: Conditional Neutrino Regression](https://mlsanity.com/paper/2207.00664/) (2022)
- [CURTAINs Flows For Flows: Constructing Unobserved Regions with Maximum Likelihood Estimation](https://mlsanity.com/paper/2305.04646/) (2023)

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

- [Convolutional L2LFlows: Generating Accurate Showers in Highly Granular Calorimeters Using Convolutional Normalizing Flows](https://mlsanity.com/paper/2405.20407/) (2024)
- [AllShowers: One model for all calorimeter showers](https://mlsanity.com/paper/2601.11716/) (2026)
- [A First Full Physics Benchmark for Highly Granular Calorimeter Surrogates](https://mlsanity.com/paper/2511.17293/) (2025)
- [Factorizable Normalizing Flows for parameter-dependent density morphing](https://mlsanity.com/paper/2606.30489/) (2026)
- [Inherited or produced? Inferring protein production kinetics when protein counts are shaped by a cell's division history](https://mlsanity.com/paper/2506.09374/) (2025)
- [Distributional Sensitivity Analysis: Enabling Differentiability in Sample-Based Inference](https://mlsanity.com/paper/2508.09347/) (2025)

## Abstract (arXiv)

There have been many applications of deep neural networks to detector calibrations and a growing number of studies that propose deep generative models as automated fast detector simulators. We show that these two tasks can be unified by using maximum likelihood estimation (MLE) from conditional generative models for energy regression. Unlike direct regression techniques, the MLE approach is prior-independent and non-Gaussian resolutions can be determined from the shape of the likelihood near the maximum. Using an ATLAS-like calorimeter simulation, we demonstrate this concept in the context of calorimeter energy calibration.