# Learning to Validate Generative Models: a Goodness-of-Fit Approach

arXiv: https://arxiv.org/abs/2511.09118 · HTML: https://mlsanity.com/paper/2511.09118/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 43 references that are in the map.
- First posted on arXiv 12 Nov 2025.

## Builds on (most cited first, 19 of 19)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [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)
- [Generalization Properties of Learning with Random Features](https://mlsanity.com/paper/1602.04474/) (2016)
- [Less is More: Nystr"om Computational Regularization](https://mlsanity.com/paper/1507.04717/) (2015)
- [Kernel methods through the roof: handling billions of points efficiently](https://mlsanity.com/paper/2006.10350/) (2020)
- [CaloChallenge 2022: A Community Challenge for Fast Calorimeter Simulation](https://mlsanity.com/paper/2410.21611/) (2024)
- [Evaluating generative models in high energy physics](https://mlsanity.com/paper/2211.10295/) (2022)
- [Learning new physics efficiently with nonparametric methods](https://mlsanity.com/paper/2204.02317/) (2022)
- [Goodness of fit by Neyman-Pearson testing](https://mlsanity.com/paper/2305.14137/) (2023)
- [Fast kernel methods for Data Quality Monitoring as a goodness-of-fit test](https://mlsanity.com/paper/2303.05413/) (2023)
- [Testing the boundaries: Normalizing Flows for higher dimensional data sets](https://mlsanity.com/paper/2202.09188/) (2022)
- [Multiple testing for signal-agnostic searches of new physics with machine learning](https://mlsanity.com/paper/2408.12296/) (2024)
- [Comparison of Affine and Rational Quadratic Spline Coupling and Autoregressive Flows through Robust Statistical Tests](https://mlsanity.com/paper/2302.12024/) (2023)
- [A Comprehensive Evaluation of Generative Models in Calorimeter Shower Simulation](https://mlsanity.com/paper/2406.12898/) (2024)
- [Calibrating Bayesian Generative Machine Learning for Bayesiamplification](https://mlsanity.com/paper/2408.00838/) (2024)
- [Comparing Generative Models with the New Physics Learning Machine](https://mlsanity.com/paper/2508.02275/) (2025)
- [The NFLikelihood: an unsupervised DNNLikelihood from Normalizing Flows](https://mlsanity.com/paper/2309.09743/) (2023)

## Built on by (most cited first, 4 of 4)

- [Neural Scaling Laws for Jet Generation](https://mlsanity.com/paper/2605.28940/) (2026)
- [SURFing to the Fundamental Limit of Jet Tagging](https://mlsanity.com/paper/2511.15779/) (2025)
- [Generative Models and Statistical Validation](https://mlsanity.com/paper/2605.30453/) (2026)
- [Are We Ready for AI-Driven Discovery? AI Verification Before the Next Fundamental Physics Breakthrough](https://mlsanity.com/paper/2607.10039/) (2026)

## Abstract (arXiv)

Generative models are increasingly central to scientific workflows, yet their systematic use and interpretation require a proper understanding of their limitations through rigorous validation. Classic approaches struggle with scalability, statistical power, or interpretability when applied to high-dimensional data, making it difficult to certify the reliability of these models in realistic, high-dimensional scientific settings. Here, we propose the use of the New Physics Learning Machine (NPLM), a learning-based approach to goodness-of-fit testing inspired by the Neyman--Pearson construction, to test generative networks trained on high-dimensional scientific data. We demonstrate the performance of NPLM for validation in two benchmark cases: generative models trained on mixtures of Gaussian models with increasing dimensionality, and a public end-to-end model, known as FlowSim, developed to generate high-energy physics collision events. We demonstrate that the NPLM can serve as a powerful validation method while also providing a means to diagnose sub-optimally modeled regions of the data.