# Scendi Score: Prompt-Aware Diversity Evaluation via Schur Complement of CLIP Embeddings

arXiv: https://arxiv.org/abs/2412.18645 · HTML: https://mlsanity.com/paper/2412.18645/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 52 references that are in the map.
- First posted on arXiv 24 Dec 2024.

## Builds on (most cited first, 30 of 35)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [DiffusionCLIP: Text-Guided Diffusion Models for Robust Image Manipulation](https://mlsanity.com/paper/2110.02711/) (2021)
- [Transformer Interpretability Beyond Attention Visualization](https://mlsanity.com/paper/2012.09838/) (2020)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [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)
- [Interpreting CLIP's Image Representation via Text-Based Decomposition](https://mlsanity.com/paper/2310.05916/) (2023)
- [Holistic Evaluation of Text-To-Image Models](https://mlsanity.com/paper/2311.04287/) (2023)
- [Interpreting CLIP with Sparse Linear Concept Embeddings (SpLiCE)](https://mlsanity.com/paper/2402.10376/) (2024)
- [Kandinsky: an Improved Text-to-Image Synthesis with Image Prior and Latent Diffusion](https://mlsanity.com/paper/2310.03502/) (2023)
- [Disentangling visual and written concepts in CLIP](https://mlsanity.com/paper/2206.07835/) (2022)
- [The Double-Ellipsoid Geometry of CLIP](https://mlsanity.com/paper/2411.14517/) (2024)
- [Consistency-diversity-realism Pareto fronts of conditional image generative models](https://mlsanity.com/paper/2406.10429/) (2024)
- [Towards a Scalable Reference-Free Evaluation of Generative Models](https://mlsanity.com/paper/2407.02961/) (2024)
- [Cousins Of The Vendi Score: A Family Of Similarity-Based Diversity Metrics For Science And Machine Learning](https://mlsanity.com/paper/2310.12952/) (2023)
- [Improving Geo-diversity of Generated Images with Contextualized Vendi Score Guidance](https://mlsanity.com/paper/2406.04551/) (2024)
- [On the Evaluation of Conditional GANs](https://mlsanity.com/paper/1907.08175/) (2019)
- [An Interpretable Evaluation of Entropy-based Novelty of Generative Models](https://mlsanity.com/paper/2402.17287/) (2024)
- [Unveiling Differences in Generative Models: A Scalable Differential Clustering Approach](https://mlsanity.com/paper/2405.02700/) (2024)
- [Be More Diverse than the Most Diverse: Optimal Mixtures of Generative Models via Mixture-UCB Bandit Algorithms](https://mlsanity.com/paper/2412.17622/) (2024)

## Built on by (most cited first, 15 of 15)

- [Kernel-based Unsupervised Embedding Alignment for Enhanced Visual Representation in Vision-language Models](https://mlsanity.com/paper/2506.02557/) (2025)
- [SPARKE: Scalable Prompt-Aware Diversity and Novelty Guidance in Diffusion Models via RKE Score](https://mlsanity.com/paper/2506.10173/) (2025)
- [Towards an Explainable Comparison and Alignment of Feature Embeddings](https://mlsanity.com/paper/2506.06231/) (2025)
- [MMD Guidance: Training-Free Distribution Adaptation for Diffusion Models via Maximum Mean Discrepancy Guidance](https://mlsanity.com/paper/2601.08379/) (2026)
- [The Maximum von Neumann Entropy Principle: Theory and Applications in Machine Learning](https://mlsanity.com/paper/2602.02117/) (2026)
- [DAK-UCB: Diversity-Aware Prompt Routing for LLMs and Generative Models](https://mlsanity.com/paper/2603.23140/) (2026)
- [KODA: Contrastive Representation Comparison and Alignment for Vision-Language Foundation Models](https://mlsanity.com/paper/2606.04180/) (2026)
- [Mixture-Greedy for Online Generative Model Selection: Is UCB Necessary in Diversity-Aware Multi-Armed Bandits?](https://mlsanity.com/paper/2603.21716/) (2026)
- [Exploring More to Solve More: Boosting Diversity in Text Diffusion Models via Entropy-Based Guidance](https://mlsanity.com/paper/2608.00024/) (2026)
- [GASS: Geometry-Aware Spherical Sampling for Disentangled Diversity Enhancement in Text-to-Image Generation](https://mlsanity.com/paper/2602.17200/) (2026)
- [Measuring What Matters Beyond Text: Evaluating Multimodal Summaries by Quality, Alignment, and Diversity](https://mlsanity.com/paper/2605.11693/) (2026)
- [Your CLIP has 164 dimensions of noise: Exploring the embeddings covariance eigenspectrum of contrastively pretrained vision-language transformers](https://mlsanity.com/paper/2605.14893/) (2026)
- [Conformal Reliability: A New Evaluation Metric for Conditional Generation](https://mlsanity.com/paper/2605.30807/) (2026)
- [Do Large Language Models Capture the Diversity in their Training Data?](https://mlsanity.com/paper/2609.02275/) (2026)
- [DiVid: Diagnosing Dimension-Specific Diversity Collapse in Video Generation Models](https://mlsanity.com/paper/2610.01661/) (2026)

## Abstract (arXiv)

The use of CLIP embeddings to assess the fidelity of samples produced by text-to-image generative models has been extensively explored in the literature. While the widely adopted CLIPScore, derived from the cosine similarity of text and image embeddings, effectively measures the alignment of a generated image, it does not quantify the diversity of images generated by a text-to-image model. In this work, we extend the application of CLIP embeddings to quantify and interpret the intrinsic diversity of text-to-image models, which are responsible for generating diverse images from similar text prompts, which we refer to as prompt-aware diversity. To achieve this, we propose a decomposition of the CLIP-based kernel covariance matrix of image data into text-based and non-text-based components. Using the Schur complement of the joint image-text kernel covariance matrix, we perform this decomposition and define the matrix-based entropy of the decomposed component as the Schur Complement ENtopy DIversity (Scendi) score, as a measure of the prompt-aware diversity for prompt-guided generative models. Additionally, we discuss the application of the Schur complement-based decomposition to nullify the influence of a given prompt on the CLIP embedding of an image, enabling focus or defocus of the embedded vectors on specific objects. We present several numerical results that apply our proposed Scendi score to evaluate text-to-image and LLM (text-to-text) models. Our numerical results indicate the success of the Scendi score in capturing the intrinsic diversity of prompt-guided generative models. The codebase is available at https://github.com/aziksh-ospanov/scendi-score.