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 notions of 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.

翻译：生成模型因其捕捉高维复杂分布的能力（如照片级图像、蛋白质结构和连接组），在众多科学领域中具有不可估量的价值。我们如何评估这些模型生成的样本？本文旨在为理解常见的统计距离概念提供易于入门的切入点，仅需基础的数学与统计学知识即可。我们聚焦于四种代表不同方法论且广泛使用的统计距离：使用低维投影（切片Wasserstein距离；SW）、通过分类器获得距离（分类器双样本检验；C2ST）、利用核的嵌入（最大均值差异；MMD）或神经网络（弗雷歇初始距离；FID）。我们阐释每种距离背后的直观原理，并说明其优点、可扩展性、复杂性和潜在陷阱。为演示这些距离在实际中的应用，我们评估了来自不同科学领域的生成模型，即一个决策模型和一个医学图像生成模型。我们展示了不同统计距离在相似数据上可能得出不同结果。通过本指南，我们旨在帮助研究人员在科学领域中正确使用、解读和评估生成模型的统计距离。