# A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Science

arXiv: https://arxiv.org/abs/2403.12636 · HTML: https://mlsanity.com/paper/2403.12636/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 109 of its 220 references that are in the map.
- First posted on arXiv 19 Mar 2024.

## Builds on (most cited first, 30 of 109)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [ChestX-ray8: Hospital-scale Chest X-ray Database and Benchmarks on Weakly-Supervised Classification and Localization of Common Thorax Diseases](https://mlsanity.com/paper/1705.02315/) (2017)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [MAUVE: Measuring the Gap Between Neural Text and Human Text using Divergence Frontiers](https://mlsanity.com/paper/2102.01454/) (2021)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)

## Built on by (most cited first, 14 of 14)

- [A Generative Framework for Probabilistic, Spatiotemporally Coherent Downscaling of Climate Simulation](https://mlsanity.com/paper/2412.15361/) (2024)
- [Compositional simulation-based inference for time series](https://mlsanity.com/paper/2411.02728/) (2024)
- [Simulation-based Bayesian inference under model misspecification](https://mlsanity.com/paper/2503.12315/) (2025)
- [Cascaded Flow Matching for Heterogeneous Tabular Data with Mixed-Type Features](https://mlsanity.com/paper/2601.22816/) (2026)
- [Using matrix-product states for time-series machine learning](https://mlsanity.com/paper/2412.15826/) (2024)
- [SMRS: advocating a unified reporting standard for surrogate models in the artificial intelligence era](https://mlsanity.com/paper/2502.06753/) (2025)
- [A Study of Posterior Stability for Time-Series Latent Diffusion](https://mlsanity.com/paper/2405.14021/) (2024)
- [What's Wrong with Your Synthetic Tabular Data? Using Explainable AI to Evaluate Generative Models](https://mlsanity.com/paper/2504.20687/) (2025)
- [Predictive posterior sampling from non-stationnary Gaussian process priors via Diffusion models with application to climate data](https://mlsanity.com/paper/2505.24556/) (2025)
- [Multivariate Uncertainty Quantification with Tomographic Quantile Forests](https://mlsanity.com/paper/2512.16383/) (2025)
- [Distribution-free two-sample testing with blurred total variation distance](https://mlsanity.com/paper/2602.05862/) (2026)
- [Classical and quantum kernel fusion for two-sample testing](https://mlsanity.com/paper/2511.20941/) (2025)
- [APEX: Assumption-free Projection-based Embedding eXamination Metric for Generative Distribution Evaluation](https://mlsanity.com/paper/2605.07786/) (2026)
- [Inverse Design for Conditional Distribution Matching](https://mlsanity.com/paper/2605.09439/) (2026)

## Abstract (arXiv)

Generative models are invaluable in many fields of science because of their ability to capture high-dimensional and complicated distributions, such as photo-realistic images, protein structures, and connectomes. How do we evaluate the samples these models generate? This work aims to provide an accessible entry point to understanding popular sample-based statistical distances, requiring only foundational knowledge in mathematics and statistics. We focus on four commonly used notions of statistical distances representing different methodologies: Using low-dimensional projections (Sliced-Wasserstein; SW), obtaining a distance using classifiers (Classifier Two-Sample Tests; C2ST), using embeddings through kernels (Maximum Mean Discrepancy; MMD), or neural networks (Fr'echet Inception Distance; FID). We highlight the intuition behind each distance and explain their merits, scalability, complexity, and pitfalls. To demonstrate how these distances are used in practice, we evaluate generative models from different scientific domains, namely a model of decision-making and a model generating medical images. We showcase that distinct distances can give different results on similar data. Through this guide, we aim to help researchers to use, interpret, and evaluate statistical distances for generative models in science.