# Cousins Of The Vendi Score: A Family Of Similarity-Based Diversity Metrics For Science And Machine Learning

arXiv: https://arxiv.org/abs/2310.12952 · HTML: https://mlsanity.com/paper/2310.12952/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 76 references that are in the map.
- First posted on arXiv 19 Oct 2023.

## Builds on (most cited first, 30 of 46)

- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Diversity is All You Need: Learning Skills without a Reward Function](https://mlsanity.com/paper/1802.06070/) (2018)
- [Autoregressive Image Generation using Residual Quantization](https://mlsanity.com/paper/2203.01941/) (2022)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Conditional Image Synthesis With Auxiliary Classifier GANs](https://mlsanity.com/paper/1610.09585/) (2016)
- [StyleGAN-XL: Scaling StyleGAN to Large Diverse Datasets](https://mlsanity.com/paper/2202.00273/) (2022)
- [Scaling up GANs for Text-to-Image Synthesis](https://mlsanity.com/paper/2303.05511/) (2023)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [The Vendi Score: A Diversity Evaluation Metric for Machine Learning](https://mlsanity.com/paper/2210.02410/) (2022)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Unsupervised Quality Estimation for Neural Machine Translation](https://mlsanity.com/paper/2005.10608/) (2020)
- [Projected GANs Converge Faster](https://mlsanity.com/paper/2111.01007/) (2021)
- [Diffusion-GAN: Training GANs with Diffusion](https://mlsanity.com/paper/2206.02262/) (2022)
- [Exposing flaws of generative model evaluation metrics and their unfair treatment of diffusion models](https://mlsanity.com/paper/2306.04675/) (2023)
- [StyleSwin: Transformer-based GAN for High-resolution Image Generation](https://mlsanity.com/paper/2112.10762/) (2021)
- [Mixture Models for Diverse Machine Translation: Tricks of the Trade](https://mlsanity.com/paper/1902.07816/) (2019)
- [PFGM++: Unlocking the Potential of Physics-Inspired Generative Models](https://mlsanity.com/paper/2302.04265/) (2023)

## Built on by (most cited first, 24 of 24)

- [Beyond Aesthetics: Cultural Competence in Text-to-Image Models](https://mlsanity.com/paper/2407.06863/) (2024)
- [Towards a Scalable Reference-Free Evaluation of Generative Models](https://mlsanity.com/paper/2407.02961/) (2024)
- [Quality-Weighted Vendi Scores And Their Application To Diverse Experimental Design](https://mlsanity.com/paper/2405.02449/) (2024)
- [Scendi Score: Prompt-Aware Diversity Evaluation via Schur Complement of CLIP Embeddings](https://mlsanity.com/paper/2412.18645/) (2024)
- [Vendi-RAG: Adaptively Trading-Off Diversity And Quality Significantly Improves Retrieval Augmented Generation With LLMs](https://mlsanity.com/paper/2502.11228/) (2025)
- [Do Vendi Scores Converge with Finite Samples? Truncated Vendi Score for Finite-Sample Convergence Guarantees](https://mlsanity.com/paper/2410.21719/) (2024)
- [DMLR: Data-centric Machine Learning Research -- Past, Present and Future](https://mlsanity.com/paper/2311.13028/) (2023)
- [Towards an Explainable Comparison and Alignment of Feature Embeddings](https://mlsanity.com/paper/2506.06231/) (2025)
- [Conditional Vendi Score: Prompt-Aware Diversity Evaluation for Generative AI Models and LLMs](https://mlsanity.com/paper/2411.02817/) (2024)
- [GRADE: Quantifying Sample Diversity in Text-to-Image Models](https://mlsanity.com/paper/2410.22592/) (2024)
- [The Alpha-Alternator: Dynamic Adaptation To Varying Noise Levels In Sequences Using The Vendi Score For Improved Robustness and Performance](https://mlsanity.com/paper/2502.04593/) (2025)
- [The Vendiscope: An Algorithmic Microscope For Data Collections](https://mlsanity.com/paper/2502.10828/) (2025)
- [Generative Adversarial Post-Training Mitigates Reward Hacking in Live Human-AI Music Interaction](https://mlsanity.com/paper/2511.17879/) (2025)
- [Assessing Domain-Level Susceptibility to Emergent Misalignment from Narrow Finetuning](https://mlsanity.com/paper/2602.00298/) (2026)
- [The Maximum von Neumann Entropy Principle: Theory and Applications in Machine Learning](https://mlsanity.com/paper/2602.02117/) (2026)
- [MS-DPPs: Multi-Source Determinantal Point Processes for Contextual Diversity Refinement of Composite Attributes in Text to Image Retrieval](https://mlsanity.com/paper/2507.06654/) (2025)
- [Vendi Novelty Scores for Out-of-Distribution Detection](https://mlsanity.com/paper/2602.10062/) (2026)
- [LatentCRF: Continuous CRF for Efficient Latent Diffusion](https://mlsanity.com/paper/2412.18596/) (2024)
- [Vendi Information Gain for Active Learning and its Application to Ecology](https://mlsanity.com/paper/2509.10390/) (2025)
- [Which Similarity-Sensitive Entropy (Sentropy)?](https://mlsanity.com/paper/2511.03849/) (2025)
- [GASS: Geometry-Aware Spherical Sampling for Disentangled Diversity Enhancement in Text-to-Image Generation](https://mlsanity.com/paper/2602.17200/) (2026)
- [More Is Not More: What Matters for Diversity in LLM Opinions?](https://mlsanity.com/paper/2607.20429/) (2026)
- [Evaluating the Diversity of AI-Generated Content with Diversity Profiles](https://mlsanity.com/paper/2608.17731/) (2026)
- [Towards Scalable Data Diversification for Language Model Pretraining via Leverage Score Sampling](https://mlsanity.com/paper/2609.32484/) (2026)

## Abstract (arXiv)

Measuring diversity accurately is important for many scientific fields, including machine learning (ML), ecology, and chemistry. The Vendi Score was introduced as a generic similarity-based diversity metric that extends the Hill number of order q=1 by leveraging ideas from quantum statistical mechanics. Contrary to many diversity metrics in ecology, the Vendi Score accounts for similarity and does not require knowledge of the prevalence of the categories in the collection to be evaluated for diversity. However, the Vendi Score treats each item in a given collection with a level of sensitivity proportional to the item's prevalence. This is undesirable in settings where there is a significant imbalance in item prevalence. In this paper, we extend the other Hill numbers using similarity to provide flexibility in allocating sensitivity to rare or common items. This leads to a family of diversity metrics -- Vendi scores with different levels of sensitivity -- that can be used in a variety of applications. We study the properties of the scores in a synthetic controlled setting where the ground truth diversity is known. We then test their utility in improving molecular simulations via Vendi Sampling. Finally, we use the Vendi scores to better understand the behavior of image generative models in terms of memorization, duplication, diversity, and sample quality.