Audio synthesizer inversion in symmetric parameter spaces with approximately equivariant flow matching

TL;DR

This paper addresses the challenge of inverting audio synthesizers by leveraging symmetry-aware probabilistic models, notably permutation equivariant flows, to improve parameter recovery in complex, real-world synthesizers.

Contribution

It introduces a symmetry-aware generative modeling approach, including a relaxed equivariance strategy, to better invert synthesizers considering their intrinsic symmetries.

Findings

Permutation-invariant regression degrades performance.

Conditional generative models improve inversion accuracy.

Permutation equivariant flows outperform baselines on real synthesizer.

Abstract

Many audio synthesizers can produce the same signal given different parameter configurations, meaning the inversion from sound to parameters is an inherently ill-posed problem. We show that this is largely due to intrinsic symmetries of the synthesizer, and focus in particular on permutation invariance. First, we demonstrate on a synthetic task that regressing point estimates under permutation symmetry degrades performance, even when using a permutation-invariant loss function or symmetry-breaking heuristics. Then, viewing equivalent solutions as modes of a probability distribution, we show that a conditional generative model substantially improves performance. Further, acknowledging the invariance of the implicit parameter distribution, we find that performance is further improved by using a permutation equivariant continuous normalizing flow. To accommodate intricate symmetries in real synthesizers, we also propose a relaxed equivariance strategy that adaptively discovers relevant symmetries from data. Applying our method to Surge XT, a full-featured open source synthesizer used in real world audio production, we find our method outperforms regression and generative baselines across audio reconstruction metrics.