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

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.