Sobolev Norms in Neural Embeddings Measure Audio Morphing Regularity

2026-10-06

AI Summary

This study addresses the lack of effective objective evaluation metrics for audio morphing trajectories within perceptual embedding spaces, where existing methods struggle to distinguish between desirable and adversarial trajectories. To overcome this limitation, this work proposes the SDIM metric, which introduces the Sobolev distance into audio morphing evaluation for the first time. By integrating physics-based sound synthesizers with neural embedding space analysis, the method leverages the Sobolev norm to quantify the regularity of morphing trajectories. Experimental results demonstrate that SDIM reliably differentiates desirable from adversarial morphing trajectories, effectively overcoming the limitations of existing metrics. Furthermore, it outperforms current state-of-the-art approaches, establishing a new paradigm for evaluating audio morphing quality.

Abstract

Morphing has recently gained renewed interest with the emergence of generative models, particularly in audio and image generation. In musical sound synthesis, morphing can generate intermediate sounds between two targets, helping musicians and sound engineers explore new sounds with interesting perceptual properties. As morphing is inherently defined in perceptual terms, evaluating this task is challenging. In this work, we introduce Sobolev Distances to Ideal Morphing (SDIM), a novel objective metric to quantify the regularity of audio morphing trajectories in perceptually relevant audio embedding spaces. Leveraging a physics-based sound synthesizer, we evaluate the discriminative power of SDIM on controlled morphing trajectories with varying degrees of regularity and compare it with that of existing audio morphing metrics. Results show that, contrary to state-of-the-art metrics, the proposed metric reliably discriminates desirable trajectories from adversarial ones.

Problem

• Audio Morphing
• Evaluation Metric
• Perceptual Embedding
• Trajectory Regularity

Innovation

• Sobolev Norms
• Audio Morphing
• Neural Embeddings
• Objective Metric
• Sound Synthesis