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

arXiv: https://arxiv.org/abs/2605.10398 · HTML: https://mlsanity.com/paper/2605.10398/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 21 of its 36 references that are in the map.
- First posted on arXiv 11 May 2026.

## Placed in

- Diffusion models / [Audio, speech and music](https://mlsanity.com/diffusion/audio-speech-and-music/)

## Builds on (most cited first, 21 of 21)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Pyroomacoustics: A Python package for audio room simulations and array processing algorithms](https://mlsanity.com/paper/1710.04196/) (2017)
- [Learning Neural Acoustic Fields](https://mlsanity.com/paper/2204.00628/) (2022)
- [Solving Audio Inverse Problems with a Diffusion Model](https://mlsanity.com/paper/2210.15228/) (2022)
- [FAST-RIR: Fast neural diffuse room impulse response generator](https://mlsanity.com/paper/2110.04057/) (2021)
- [An Introduction to Flow Matching and Diffusion Models](https://mlsanity.com/paper/2506.02070/) (2025)
- [Sound field reconstruction in rooms: inpainting meets super-resolution](https://mlsanity.com/paper/2001.11263/) (2020)
- [Generative Data Augmentation Challenge: Synthesis of Room Acoustics for Speaker Distance Estimation](https://mlsanity.com/paper/2501.13250/) (2025)
- [Reconstruction of Sound Field through Diffusion Models](https://mlsanity.com/paper/2312.08821/) (2023)
- [Physics-Informed Neural Network for Volumetric Sound field Reconstruction of Speech Signals](https://mlsanity.com/paper/2403.09524/) (2024)
- [Generative adversarial networks with physical sound field priors](https://mlsanity.com/paper/2308.00426/) (2023)
- [Gencho: Room Impulse Response Generation from Reverberant Speech and Text via Diffusion Transformers](https://mlsanity.com/paper/2602.09233/) (2026)
- [Room Impulse Response Generation Conditioned on Acoustic Parameters](https://mlsanity.com/paper/2507.12136/) (2025)
- [Sound field reconstruction using neural processes with dynamic kernels](https://mlsanity.com/paper/2311.05188/) (2023)
- [Sound Field Reconstruction Using Physics-Informed Boundary Integral Networks](https://mlsanity.com/paper/2506.03917/) (2025)
- [Solving Room Impulse Response Inverse Problems Using Flow Matching with Analytic Wiener Denoiser](https://mlsanity.com/paper/2602.00652/) (2026)
- [Few-shot Acoustic Synthesis with Multimodal Flow Matching](https://mlsanity.com/paper/2603.19176/) (2026)
- [Learning Magnitude Distribution of Sound Fields via Conditioned Autoencoder](https://mlsanity.com/paper/2506.16729/) (2025)

## Abstract (arXiv)

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 SI1kHz, trains substantially faster than the autoencoder baseline, and improves significantly with dataset size.