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

TL;DR

RIRFlow addresses the ill-posed problem of room impulse response estimation without data-driven priors by marrying flow matching with an analytic MMSE Wiener denoiser derived from an exponentially decaying Gaussian RIR model. The single-band prior is $d_k(\lambda,\alpha)=\alpha^2 e^{-2\lambda k}$, enabling closed-form denoising and a grid-based Bayesian averaging over $\lambda$ to build a multi-band denoiser used within the FLOWER framework. The method extends to nonlinear/non-Gaussian settings via a local Gaussian approximation of the guided posterior and applies a common proximal refinement to denoise, deconvolve, inpaint, and declip RIRs. Experiments on real RIRs across five inverse problems show robust, stable reconstructions and improved performance over baselines, highlighting the benefit of integrating classic RIR modeling with flow-based inference in a training-free solver.

Abstract

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.

Figures (15)

• Figure 1: Illustration of RIRFlow. The algorithm starts from an initial noise sample $\mathbf{x}_0 \sim p_0$ and iteratively applies denoising followed by measurement refinement. Through this process, it yields a sample $\mathbf{x}_1 \sim p_1$ that is consistent with both the RIR prior and the observed measurement.
• Figure 2: Example of a cropped RIR ("h054_Kitchen_3txts") for an inpainting problem.
• Figure 3: Example of a measurement signal that is clipped. The convolved signal (top) is hard clipped and is contaminated with noise (bottom).
• Figure 4: EDCs for the denoising experiment on the RIR "h054_Kitchen_3txts" corrupted by Gaussian measurement noise with an SNR of 30 dB.
• Figure 5: ST-NMSE for the denoising task on the RIR "h054_Kitchen_3txts" corrupted by Gaussian measurement noise with an SNR of 30 dB, cf. Fig. \ref{['fig:denoising_example']}. Lower values correspond to more accurate energy reconstruction.