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Paper · 2506.07199 · 2025

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

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 6 functions out of this paper's own repositories and ran 5 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
ben-hayes/synth-permutations canonical 5 of 6
FunctionStatusWhere it lives
call_with_cfg Ran ben-hayes/synth-permutations/src/models/ksin_flow_matching_module.py
code served (permissive licence) · get_code("7260bb800f58b225")
call_with_cfg Ran ben-hayes/synth-permutations/src/models/surge_flow_matching_module.py
code served (permissive licence) · get_code("a65643f216e2baa0")
complex_to_dbfs Ran ben-hayes/synth-permutations/src/metrics.py
code served (permissive licence) · get_code("eb983451c0d56c12")
late_curve Ran ben-hayes/synth-permutations/src/models/ksin_flow_matching_module.py
code served (permissive licence) · get_code("a5566930666141a9")
rk4_with_cfg Ran ben-hayes/synth-permutations/src/models/surge_flow_matching_module.py
code served (permissive licence) · get_code("4bbc07cdc627f03f")
cosine_curve Not yet run ben-hayes/synth-permutations/src/models/ksin_flow_matching_module.py
code served (permissive licence) · get_code("7c8e3e7135006f03")

Repositories linked to this paper

Some links come from the archived Papers with Code dataset (CC BY-SA 4.0): attribution and licence.

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.

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