An end-to-end framework for uncertainty-aware validation of generative models
Abstract
Density estimation with generative models is a common task in the physical sciences, for example in background estimation in particle physics. Existing machine learning techniques, however, lack methods to quantify uncertainties that can be propagated into a statistical test. That limits the validation of generative models to standard goodness-of-fit tests, in which the generative model is treated as exact (point-null hypothesis). But a model fitted to a finite training set is never exact, so if its uncertainties are neglected, any sufficiently powerful goodness-of-fit test will eventually reject it once the test set is large enough to resolve this estimation error. We propose SIGMA, an end-to-end framework combining density estimation with principled uncertainty quantification. We use Gaussian mixture models, for which uncertainties are tractable, and further construct a new goodness-of-fit test in which these uncertainties are profiled as nuisance parameters to account for the statistical error of the fit, promoting the conventional point-null test to a composite one. A rejection then signals genuine mismodeling rather than a test set large enough to resolve the error of the fit, provided the propagated uncertainties faithfully cover that error. We demonstrate the framework on a controlled two-dimensional toy model and on a collider physics benchmark modeling the QCD background process. With uncertainties included, the same model can be trusted on test sets up to an order of magnitude larger than the standard test allows. Our work thus provides a statistically grounded basis for a robust use of generative models in the physical sciences.
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BibTeX
@misc{badaracco2026endtoend,
title = {{An end-to-end framework for uncertainty-aware validation of generative models}},
author = {Giada Badaracco and Sean Benevedes and Christina Reissel and Philip Harris and Gaia Grosso},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37398},
eprint = {2610.37398},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37398},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An end-to-end framework for uncertainty-aware validation of generative models
AU - Giada Badaracco
AU - Sean Benevedes
AU - Christina Reissel
AU - Philip Harris
AU - Gaia Grosso
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37398
UR - https://arxiv.org/abs/2610.37398
AB - Density estimation with generative models is a common task in the physical sciences, for example in background estimation in particle physics. Existing machine learning techniques, however, lack methods to quantify uncertainties that can be propagated into a statistical test. That limits the validation of generative models to standard goodness-of-fit tests, in which the generative model is treated as exact (point-null hypothesis). But a model fitted to a finite training set is never exact, so if its uncertainties are neglected, any sufficiently powerful goodness-of-fit test will eventually reject it once the test set is large enough to resolve this estimation error. We propose SIGMA, an end-to-end framework combining density estimation with principled uncertainty quantification. We use Gaussian mixture models, for which uncertainties are tractable, and further construct a new goodness-of-fit test in which these uncertainties are profiled as nuisance parameters to account for the statistical error of the fit, promoting the conventional point-null test to a composite one. A rejection then signals genuine mismodeling rather than a test set large enough to resolve the error of the fit, provided the propagated uncertainties faithfully cover that error. We demonstrate the framework on a controlled two-dimensional toy model and on a collider physics benchmark modeling the QCD background process. With uncertainties included, the same model can be trusted on test sets up to an order of magnitude larger than the standard test allows. Our work thus provides a statistically grounded basis for a robust use of generative models in the physical sciences.
ER -