# Calibrating Bayesian Generative Machine Learning for Bayesiamplification

arXiv: https://arxiv.org/abs/2408.00838 · HTML: https://mlsanity.com/paper/2408.00838/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 1 Aug 2024.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Bayesian Neural Networks: An Introduction and Survey](https://mlsanity.com/paper/2006.12024/) (2020)
- [Specifying Weight Priors in Bayesian Deep Neural Networks with Empirical Bayes](https://mlsanity.com/paper/1906.05323/) (2019)
- [GANplifying Event Samples](https://mlsanity.com/paper/2008.06545/) (2020)
- [CaloClouds II: Ultra-Fast Geometry-Independent Highly-Granular Calorimeter Simulation](https://mlsanity.com/paper/2309.05704/) (2023)
- [Understanding Event-Generation Networks via Uncertainties](https://mlsanity.com/paper/2104.04543/) (2021)
- [EPiC-ly Fast Particle Cloud Generation with Flow-Matching and Diffusion](https://mlsanity.com/paper/2310.00049/) (2023)
- [Latent Space Refinement for Deep Generative Models](https://mlsanity.com/paper/2106.00792/) (2021)
- [Interpretable Uncertainty Quantification in AI for HEP](https://mlsanity.com/paper/2208.03284/) (2022)
- [Bayesian Neural Networks for Fast SUSY Predictions](https://mlsanity.com/paper/2007.04506/) (2020)
- [AdamMCMC: Combining Metropolis Adjusted Langevin with Momentum-based Optimization](https://mlsanity.com/paper/2312.14027/) (2023)

## Built on by (most cited first, 5 of 5)

- [Learning to Validate Generative Models: a Goodness-of-Fit Approach](https://mlsanity.com/paper/2511.09118/) (2025)
- [Forecasting Generative Amplification](https://mlsanity.com/paper/2509.08048/) (2025)
- [Uncertainty in Physics and AI: Taxonomy, Quantification, and Validation](https://mlsanity.com/paper/2605.10378/) (2026)
- [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)

## Abstract (arXiv)

Recently, combinations of generative and Bayesian machine learning have been introduced in particle physics for both fast detector simulation and inference tasks. These neural networks aim to quantify the uncertainty on the generated distribution originating from limited training statistics. The interpretation of a distribution-wide uncertainty however remains ill-defined. We show a clear scheme for quantifying the calibration of Bayesian generative machine learning models. For a Continuous Normalizing Flow applied to a low-dimensional toy example, we evaluate the calibration of Bayesian uncertainties from either a mean-field Gaussian weight posterior, or Monte Carlo sampling network weights, to gauge their behaviour on unsteady distribution edges. Well calibrated uncertainties can then be used to roughly estimate the number of uncorrelated truth samples that are equivalent to the generated sample and clearly indicate data amplification for smooth features of the distribution.