# APEX: Assumption-free Projection-based Embedding eXamination Metric for Generative Distribution Evaluation

arXiv: https://arxiv.org/abs/2605.07786 · HTML: https://mlsanity.com/paper/2605.07786/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 38 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 23 of 23)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [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)
- [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)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [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)
- [A note on the evaluation of generative models](https://mlsanity.com/paper/1511.01844/) (2015)
- [Exposing flaws of generative model evaluation metrics and their unfair treatment of diffusion models](https://mlsanity.com/paper/2306.04675/) (2023)
- [A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Science](https://mlsanity.com/paper/2403.12636/) (2024)
- [Fr'echet Wavelet Distance: A Domain-Agnostic Metric for Image Generation](https://mlsanity.com/paper/2312.15289/) (2023)

## Abstract (arXiv)

As generative models achieve unprecedented visual quality, the gold standard for image evaluation remains traditional feature-distribution metrics. However, these metrics are provably hindered by the closed-vocabulary bottleneck of outdated features and the assumptive bias of rigid parametric formulations. Recent alternatives exploit modern backbones to solve the feature bottleneck, yet continue to suffer from parametric limitations. To close this gap, we introduce APEX (Assumption-free Projection-based Embedding eXamination), a novel evaluation framework leveraging two open-vocabulary foundation models (CLIP and DINOv2) as feature extractors and the Sliced Wasserstein Distance (SWD) as similarity measure. Since SWD requires no assumptions about the compared data distributions, APEX operates as an assumption-free metric. Moreover, we prove with theoretical and empirical evidences that it inherits effective scalability to high-dimensional spaces. Benchmarking APEX metrics against established baselines, we show that they exhibit strong robustness to visual degradations, intra- and cross-dataset stability, ensuring highly stable evaluations on out-of-domain datasets.