# Solving Room Impulse Response Inverse Problems Using Flow Matching with Analytic Wiener Denoiser

arXiv: https://arxiv.org/abs/2602.00652 · HTML: https://mlsanity.com/paper/2602.00652/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 25 of its 54 references that are in the map.
- First posted on arXiv 31 Jan 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 25 of 25)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [TFG: Unified Training-Free Guidance for Diffusion Models](https://mlsanity.com/paper/2409.15761/) (2024)
- [PnP-Flow: Plug-and-Play Image Restoration with Flow Matching](https://mlsanity.com/paper/2410.02423/) (2024)
- [Training-free Linear Image Inverses via Flows](https://mlsanity.com/paper/2310.04432/) (2023)
- [Solving Audio Inverse Problems with a Diffusion Model](https://mlsanity.com/paper/2210.15228/) (2022)
- [JPEG Artifact Correction using Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2209.11888/) (2022)
- [An Introduction to Flow Matching and Diffusion Models](https://mlsanity.com/paper/2506.02070/) (2025)
- [Flower: A Flow-Matching Solver for Inverse Problems](https://mlsanity.com/paper/2509.26287/) (2025)
- [Deep Impulse Responses: Estimating and Parameterizing Filters with Deep Networks](https://mlsanity.com/paper/2202.03416/) (2022)
- [Unsupervised Blind Joint Dereverberation and Room Acoustics Estimation with Diffusion Models](https://mlsanity.com/paper/2408.07472/) (2024)
- [Sound field reconstruction in rooms: inpainting meets super-resolution](https://mlsanity.com/paper/2001.11263/) (2020)
- [Room impulse response reconstruction with physics-informed deep learning](https://mlsanity.com/paper/2401.01206/) (2024)
- [The Generation Phases of Flow Matching: a Denoising Perspective](https://mlsanity.com/paper/2510.24830/) (2025)
- [Deep, data-driven modeling of room acoustics: literature review and research perspectives](https://mlsanity.com/paper/2504.16289/) (2025)
- [AnyRIR: Robust Non-intrusive Room Impulse Response Estimation in the Wild](https://mlsanity.com/paper/2510.17788/) (2025)

## Built on by (most cited first, 2 of 2)

- [Ambisonics Encoding of Room Impulse Responses using a Device-Agnostic Diffusion Model](https://mlsanity.com/paper/2608.14097/) (2026)
- [SF-Flow: Sound field magnitude estimation via flow matching guided by sparse measurements](https://mlsanity.com/paper/2605.10398/) (2026)

## Abstract (arXiv)

Room impulse response (RIR) estimation naturally arises as a class of inverse problems, including denoising and deconvolution. While recent approaches often rely on supervised learning or learned generative priors, such methods require large amounts of training data and may generalize poorly outside the training distribution. In this work, we present RIRFlow, a training-free Bayesian framework for RIR inverse problems using flow matching. We derive a flow-consistent analytic prior from the statistical structure of RIRs, eliminating the need for data-driven priors. Specifically, we model RIR as a Gaussian process with exponentially decaying variance, which yields a closed-form minimum mean squared error (MMSE) Wiener denoiser. This analytic denoiser is integrated as a prior in an existing flow-based inverse solver, where inverse problems are solved via guided posterior sampling. Furthermore, we extend the solver to nonlinear and non-Gaussian inverse problems via a local Gaussian approximation of the guided posterior, and empirically demonstrate that this approximation remains effective in practice. Experiments on real RIRs across different inverse problems demonstrate robust performance, highlighting the effectiveness of combining a classic RIR model with the recent flow-based generative inference.