# End-To-End Latent Variational Diffusion Models for Inverse Problems in High Energy Physics

arXiv: https://arxiv.org/abs/2305.10399 · HTML: https://mlsanity.com/paper/2305.10399/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 31 of its 61 references that are in the map.
- First posted on arXiv 17 May 2023.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Multimodal Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/1804.04732/) (2018)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [Stabilizing Transformers for Reinforcement Learning](https://mlsanity.com/paper/1910.06764/) (2019)
- [Equivariant 3D-Conditional Diffusion Models for Molecular Linker Design](https://mlsanity.com/paper/2210.05274/) (2022)
- [DiffuseVAE: Efficient, Controllable and High-Fidelity Generation from Low-Dimensional Latents](https://mlsanity.com/paper/2201.00308/) (2022)
- [CaloGAN: Simulating 3D High Energy Particle Showers in Multi-Layer Electromagnetic Calorimeters with Generative Adversarial Networks](https://mlsanity.com/paper/1712.10321/) (2017)
- [Score-based Generative Models for Calorimeter Shower Simulation](https://mlsanity.com/paper/2206.11898/) (2022)
- [CaloClouds: Fast Geometry-Independent Highly-Granular Calorimeter Simulation](https://mlsanity.com/paper/2305.04847/) (2023)
- [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)
- [PC-JeDi: Diffusion for Particle Cloud Generation in High Energy Physics](https://mlsanity.com/paper/2303.05376/) (2023)
- [Permutationless Many-Jet Event Reconstruction with Symmetry Preserving Attention Networks](https://mlsanity.com/paper/2010.09206/) (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)
- [SPANet: Generalized Permutationless Set Assignment for Particle Physics using Symmetry Preserving Attention](https://mlsanity.com/paper/2106.03898/) (2021)

## Built on by (most cited first, 22 of 22)

- [On the Design Fundamentals of Diffusion Models: A Survey](https://mlsanity.com/paper/2306.04542/) (2023)
- [A Lorentz-Equivariant Transformer for All of the LHC](https://mlsanity.com/paper/2411.00446/) (2024)
- [A Survey on Physics Informed Reinforcement Learning: Review and Open Problems](https://mlsanity.com/paper/2309.01909/) (2023)
- [The Landscape of Unfolding with Machine Learning](https://mlsanity.com/paper/2404.18807/) (2024)
- [Diffusion State-Guided Projected Gradient for Inverse Problems](https://mlsanity.com/paper/2410.03463/) (2024)
- [Improving new physics searches with diffusion models for event observables and jet constituents](https://mlsanity.com/paper/2312.10130/) (2023)
- [PC-Droid: Faster diffusion and improved quality for particle cloud generation](https://mlsanity.com/paper/2307.06836/) (2023)
- [Full Event Particle-Level Unfolding with Variable-Length Latent Variational Diffusion](https://mlsanity.com/paper/2404.14332/) (2024)
- [Unifying Simulation and Inference with Normalizing Flows](https://mlsanity.com/paper/2404.18992/) (2024)
- [Generative Unfolding with Distribution Mapping](https://mlsanity.com/paper/2411.02495/) (2024)
- [Generalizing to new geometries with Geometry-Aware Autoregressive Models (GAAMs) for fast calorimeter simulation](https://mlsanity.com/paper/2305.11531/) (2023)
- [Towards diffusion models for large-scale sea-ice modelling](https://mlsanity.com/paper/2406.18417/) (2024)
- [Simulation-Prior Independent Neural Unfolding Procedure](https://mlsanity.com/paper/2507.15084/) (2025)
- [Latent Representation Matters: Human-like Sketches in One-shot Drawing Tasks](https://mlsanity.com/paper/2406.06079/) (2024)
- [Extrapolating Jet Radiation with Autoregressive Transformers](https://mlsanity.com/paper/2412.12074/) (2024)
- [Generative Models and Statistical Validation](https://mlsanity.com/paper/2605.30453/) (2026)
- [Variational inference for pile-up removal at hadron colliders with diffusion models](https://mlsanity.com/paper/2410.22074/) (2024)
- [Latent Generative Modeling of Random Fields from Limited Training Data](https://mlsanity.com/paper/2505.13007/) (2025)
- [Designing Observables for Measurements with Deep Learning](https://mlsanity.com/paper/2310.08717/) (2023)
- [Towards Photonic Band Diagram Generation with Transformer-Latent Diffusion Models](https://mlsanity.com/paper/2510.01749/) (2025)
- [Machine Learning-based Unfolding for Cross Section Measurements in the Presence of Nuisance Parameters](https://mlsanity.com/paper/2512.07074/) (2025)
- [Diffusion-Driven State Space Models](https://mlsanity.com/paper/2606.21036/) (2026)

## Abstract (arXiv)

High-energy collisions at the Large Hadron Collider (LHC) provide valuable insights into open questions in particle physics. However, detector effects must be corrected before measurements can be compared to certain theoretical predictions or measurements from other detectors. Methods to solve this textitinverse problem of mapping detector observations to theoretical quantities of the underlying collision are essential parts of many physics analyses at the LHC. We investigate and compare various generative deep learning methods to approximate this inverse mapping. We introduce a novel unified architecture, termed latent variation diffusion models, which combines the latent learning of cutting-edge generative art approaches with an end-to-end variational framework. We demonstrate the effectiveness of this approach for reconstructing global distributions of theoretical kinematic quantities, as well as for ensuring the adherence of the learned posterior distributions to known physics constraints. Our unified approach achieves a distribution-free distance to the truth of over 20 times less than non-latent state-of-the-art baseline and 3 times less than traditional latent diffusion models.