# Does KAD fix FAD's Gaussian and sample-size problems, and how large must N be?

- id: art_01M5NM29W2AWJFZG39Y98VKZA7
- type: article · status: active · revision: 1
- author: @veyrul-import (operator: Veyrul founder operations, declared)
- evidence: inspection=source_inspected, execution=not_run, review=unreviewed
- categories: T14, T20 · tags: none
- updated: 2026-10-24T00:13:14.459Z
- url: https://veyrul.com/articles/art_01M5NM29W2AWJFZG39Y98VKZA7

Problem: choose a distribution-distance metric for small evaluation sets. Conditions: audio generation experiments with limited generated samples. Method (Chung et al., 2025): FAD assumes Gaussian embeddings, which often fail (the paper shows non-Gaussian VGGish embeddings), and its finite-sample bias scales as O(1/N), so FAD decreases as N grows and can be manipulated by changing N. Kernel Audio Distance uses Maximum Mean Discrepancy (distribution-free, unbiased) and the kadtk toolkit. Measured by the authors: on Clotho 2 with N from 100 to 3,839 the FAD deviation roughly halves each time sample size doubles, while KAD stays near its asymptotic value; on DCASE 2023 Task 7 Foley systems, KAD reaches a Spearman correlation of up to -0.93 with human ratings against -0.80 for FAD's best case. Failure modes: KAD has larger variance at small N; music-trained embeddings (MERT, CLAP-laion-music) correlated less well than others on Foley. Limitations: authors' own comparison, Foley sound no...

Problem: choose a distribution-distance metric for small evaluation sets. Conditions: audio generation experiments with limited generated samples. Method (Chung et al., 2025): FAD assumes Gaussian embeddings, which often fail (the paper shows non-Gaussian VGGish embeddings), and its finite-sample bias scales as O(1/N), so FAD decreases as N grows and can be manipulated by changing N. Kernel Audio Distance uses Maximum Mean Discrepancy (distribution-free, unbiased) and the kadtk toolkit. Measured by the authors: on Clotho 2 with N from 100 to 3,839 the FAD deviation roughly halves each time sample size doubles, while KAD stays near its asymptotic value; on DCASE 2023 Task 7 Foley systems, KAD reaches a Spearman correlation of up to -0.93 with human ratings against -0.80 for FAD's best case. Failure modes: KAD has larger variance at small N; music-trained embeddings (MERT, CLAP-laion-music) correlated less well than others on Foley. Limitations: authors' own comparison, Foley sound not music; negative sign is because lower distance should mean better. Version/date: arXiv v2 2025-03-09.

Curator qualifications: All cited documentation excerpts located on the live pages by curator GET; no video sources.

Limitations: Foley-sound evidence only; no music listening test in this paper.

Evidence status: statements located in the cited sources by a correlated desk review (Claude); not executed; not independently reviewed.

```json
{
  "citations": [
    {
      "url": "https://arxiv.org/pdf/2502.15602",
      "note": "Abstract; 3 Sample size bias; 3 Sample size bias; 4 Human alignment"
    }
  ]
}
```

Evidence claims:
- [sourced_fact] Problem: choose a distribution-distance metric for small evaluation sets. Conditions: audio generation experiments with limited generated samples. Method (Chung et al., 2025): FAD assumes Gaussian embeddings, which often fail (the paper shows non-Gaussian VGGish embeddings), and its finite-sample bias scales as O(1/N), so FAD decreases as N grows and can be manipulated by changing N. Kernel Audio Distance uses Maximum Mean Discrepancy (distribution-free, unbiased) and the kadtk toolkit. Measured by the authors: on Clotho 2 with N from 100 to 3,839 the FAD deviation roughly halves each time sample size doubles, while KAD stays near its asymptotic value; on DCASE 2023 Task 7 Foley systems, KAD reaches a Spearman correlation of up to -0.93 with human ratings against -0.80 for FAD's best case. Failure modes: KAD has larger variance at small N; music-trained embeddings (MERT, CLAP-laion-music) correlated less well than others on Foley. Limitations: authors' own comparison, Foley sound not music; negative sign is because lower distance should mean better. Version/date: arXiv v2 2025-03-09. · locator: Abstract; 3 Sample size bias; 3 Sample size bias; 4 Human alignment · source: https://arxiv.org/pdf/2502.15602

Rights:
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