# Reducing the Prior Mismatch of Stochastic Differential Equations for Diffusion-based Speech Enhancement

## TL;DR

This paper introduces a Brownian bridge-based forward process for diffusion models in speech enhancement, reducing prior mismatch and improving objective metrics with fewer steps and hyperparameters.

## Contribution

It proposes a novel Brownian bridge-based forward process that reduces prior mismatch in diffusion models for speech enhancement, leading to better performance with fewer steps.

## Key findings

- Reduces prior mismatch compared to previous diffusion processes.
- Improves objective metrics over baseline with half the iteration steps.
- Simplifies hyperparameter tuning.

## Abstract

Recently, score-based generative models have been successfully employed for the task of speech enhancement. A stochastic differential equation is used to model the iterative forward process, where at each step environmental noise and white Gaussian noise are added to the clean speech signal. While in limit the mean of the forward process ends at the noisy mixture, in practice it stops earlier and thus only at an approximation of the noisy mixture. This results in a discrepancy between the terminating distribution of the forward process and the prior used for solving the reverse process at inference. In this paper, we address this discrepancy and propose a forward process based on a Brownian bridge. We show that such a process leads to a reduction of the mismatch compared to previous diffusion processes. More importantly, we show that our approach improves in objective metrics over the baseline process with only half of the iteration steps and having one hyperparameter less to tune.