cs.SDOct 6, 2026

Sobolev Norms in Neural Embeddings Measure Audio Morphing Regularity

Authors: Théo Chasle Cauchy, Modan Tailleur, Barbara Pascal, Fanny Roche, Mathieu Lagrange

Organizations: Nantes Universit´e, ´Ecole Centrale Nantes, CNRS, LS2N, UMR6004, F-44000 Nantes, France. · Arturia, Montbonnot Saint-Martin, France

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.

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