Optimal Transport Audio Distance with Learned Riemannian Ground Metrics

TL;DR

This paper introduces OTAD, a novel audio distance metric that improves evaluation accuracy by correcting primitive components with learned Riemannian metrics and entropic Sinkhorn transport, outperforming existing methods.

Contribution

It proposes a new audio distance measure, OTAD, with dedicated mechanisms for cost and coupling, enhancing evaluation precision and diagnostics over prior metrics.

Findings

OTAD outperforms FAD in coupling sensitivity by a factor of 1.9 to 3.6.

OTAD achieves higher correlation with audio MOS scores than baseline metrics.

Per-sample diagnostics with AUROC ≥ 0.86 are enabled by OTAD's discrete transport plan.

Abstract

In audio generation evaluation, Fr\'echet Audio Distance (FAD) is a 2-Wasserstein distance with structural constraints for both primitives: the cost is a frozen embedding pullback whose invariance set hides severe artifacts, and the coupling is a Gaussian fit that dilutes rank-1 contamination relative to discrete OT. We propose Optimal Transport Audio Distance (OTAD), which corrects each primitive with one dedicated mechanism -- a residual Riemannian ground-metric adapter for the cost and entropic Sinkhorn optimal transport for the coupling. Across eight encoders under a four-axis protocol, coupling-only comparisons at $\epsilon = 0.05$ show that Sinkhorn's rank-1 sensitivity exceeds FAD's by a factor of 1.9 to 3.6. Furthermore, OTAD achieves a higher mean Spearman correlation with audio-quality MOS (DCASE 2023 Task 7) than baseline metrics. As an intrinsic benefit of the discrete transport plan, OTAD yields per-sample diagnostics with AUROC $\ge 0.86$, a capability that scalar- or kernel-aggregated metrics structurally lack.