# SF-Flow: Sound field magnitude estimation via flow matching guided by sparse measurements

Source: [SF-Flow: Sound field magnitude estimation via flow matching guided by sparse measurements](<https://www.sota2.com/research/paper/6a02b47adbc836b87d824c02>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-05-13T05:00:20.520Z

Authors: Ege Erdem, Shoichi Koyama, Tomohiko Nakamura, Orchisama Das, Zoran Cvetkovi\\'c

Published: 2026-05-11T11:40:57.000Z

## Abstract

Reconstructing a 3D sound field from sparse microphone measurements is a fundamental yet ill-posed problem, which we address through Acoustic Transfer Function (ATF) magnitude estimation. ATF magnitude encapsulates key perceptual and acoustic properties of a physical space with applications in room characterization and correction. Although recent generative paradigms such as Flow Matching (FM) have achieved state-of-the-art performance in speech and music generation, their potential in spatial audio remains underexplored. We propose a novel framework for 3D ATF magnitude reconstruction as a guided generation task, with a 3D U-Net conditioned by a permutation-invariant set encoder. This architecture enables reconstruction from an arbitrary number of sparse inputs while leveraging the stable and efficient training properties of FM. Experimental results demonstrate that SF-Flow achieves accurate reconstruction up to \\SI{1}{kHz}, trains substantially faster than the autoencoder baseline, and improves significantly with dataset size.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [3D ATF reconstruction on R1 (test)](<https://www.sota2.com/research/sota/3d-atf-reconstruction-on-r1-test.md>): 3D ATF reconstruction; R1 (test); LSD (0-20 / 312 Hz): 1.76.

- [3D ATF reconstruction on R3 (test)](<https://www.sota2.com/research/sota/3d-atf-reconstruction-on-r3-test.md>): 3D ATF reconstruction; R3 (test); LSD (0-20 / 312 Hz): 0.55.

- [3D ATF reconstruction on R2 (test)](<https://www.sota2.com/research/sota/3d-atf-reconstruction-on-r2-test.md>): 3D ATF reconstruction; R2 (test); LSD (0-20 / 312 Hz): 0.78.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2605.10398>)

[PDF](<https://arxiv.org/pdf/2605.10398.pdf>)