# Reducing the Prior Mismatch of Stochastic Differential Equations for Diffusion-based Speech Enhancement arXiv: https://arxiv.org/abs/2302.14748 ยท HTML: https://mlsanity.com/paper/2302.14748/ ## Key facts - Cited by 30 papers in the map (data through 14 Oct 2026). - Placed in Audio, speech and music, one of 14 directions in Diffusion models. - Builds on 14 of its 28 references that are in the map. - First posted on arXiv 28 Feb 2023. ## Placed in - Diffusion models / [Audio, speech and music](https://mlsanity.com/diffusion/audio-speech-and-music/) ## Builds on (most cited first, 14 of 14) - [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014) - [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020) - [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020) - [Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speech](https://mlsanity.com/paper/2105.06337/) (2021) - [SDR - half-baked or well done?](https://mlsanity.com/paper/1811.02508/) (2018) - [Conv-TasNet: Surpassing Ideal Time-Frequency Magnitude Masking for Speech Separation](https://mlsanity.com/paper/1809.07454/) (2018) - [Supervised Speech Separation Based on Deep Learning: An Overview](https://mlsanity.com/paper/1708.07524/) (2017) - [Speech Enhancement and Dereverberation with Diffusion-based Generative Models](https://mlsanity.com/paper/2208.05830/) (2022) - [Conditional Diffusion Probabilistic Model for Speech Enhancement](https://mlsanity.com/paper/2202.05256/) (2022) - [Speech Enhancement with Score-Based Generative Models in the Complex STFT Domain](https://mlsanity.com/paper/2203.17004/) (2022) - [Diffusion-Based Voice Conversion with Fast Maximum Likelihood Sampling Scheme](https://mlsanity.com/paper/2109.13821/) (2021) - [The fifth 'CHiME' Speech Separation and Recognition Challenge: Dataset, task and baselines](https://mlsanity.com/paper/1803.10609/) (2018) - [Universal Speech Enhancement with Score-based Diffusion](https://mlsanity.com/paper/2206.03065/) (2022) - [A Study on Speech Enhancement Based on Diffusion Probabilistic Model](https://mlsanity.com/paper/2107.11876/) (2021) ## Built on by (most cited first, 30 of 30) - [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024) - [Diffusion Models for Audio Restoration](https://mlsanity.com/paper/2402.09821/) (2024) - [FlowSE: Flow Matching-based Speech Enhancement](https://mlsanity.com/paper/2508.06840/) (2025) - [Single and Few-step Diffusion for Generative Speech Enhancement](https://mlsanity.com/paper/2309.09677/) (2023) - [FlowDec: A flow-based full-band general audio codec with high perceptual quality](https://mlsanity.com/paper/2503.01485/) (2025) - [Investigating the Design Space of Diffusion Models for Speech Enhancement](https://mlsanity.com/paper/2312.04370/) (2023) - [Noise-robust Speech Separation with Fast Generative Correction](https://mlsanity.com/paper/2406.07461/) (2024) - [DDTSE: Discriminative Diffusion Model for Target Speech Extraction](https://mlsanity.com/paper/2309.13874/) (2023) - [SE-Bridge: Speech Enhancement with Consistent Brownian Bridge](https://mlsanity.com/paper/2305.13796/) (2023) - [EMOCONV-DIFF: Diffusion-based Speech Emotion Conversion for Non-parallel and In-the-wild Data](https://mlsanity.com/paper/2309.07828/) (2023) - [FINALLY: fast and universal speech enhancement with studio-like quality](https://mlsanity.com/paper/2410.05920/) (2024) - [Thunder : Unified Regression-Diffusion Speech Enhancement with a Single Reverse Step using Brownian Bridge](https://mlsanity.com/paper/2406.06139/) (2024) - [Diffusion Buffer: Online Diffusion-based Speech Enhancement with Sub-Second Latency](https://mlsanity.com/paper/2506.02908/) (2025) - [An Analysis of the Variance of Diffusion-based Speech Enhancement](https://mlsanity.com/paper/2402.00811/) (2024) - [Conditional Diffusion Model for Target Speaker Extraction](https://mlsanity.com/paper/2310.04791/) (2023) - [SigDiffusions: Score-Based Diffusion Models for Time Series via Log-Signature Embeddings](https://mlsanity.com/paper/2406.10354/) (2024) - [A Composite Predictive-Generative Approach to Monaural Universal Speech Enhancement](https://mlsanity.com/paper/2505.24576/) (2025) - [Schr"odinger Bridge Consistency Trajectory Models for Speech Enhancement](https://mlsanity.com/paper/2507.11925/) (2025) - [Flowing Straighter with Conditional Flow Matching for Accurate Speech Enhancement](https://mlsanity.com/paper/2508.20584/) (2025) - [Shortcut Flow Matching for Speech Enhancement: Step-Invariant flows via single stage training](https://mlsanity.com/paper/2509.21522/) (2025) - [Diffusion Buffer for Online Generative Speech Enhancement](https://mlsanity.com/paper/2510.18744/) (2025) - [Robustness of Speech Separation Models for Similar-pitch Speakers](https://mlsanity.com/paper/2407.15749/) (2024) - [Audio Generation Through Score-Based Generative Modeling: Design Principles and Implementation](https://mlsanity.com/paper/2506.08457/) (2025) - [Investigating training objective for flow matching-based speech enhancement](https://mlsanity.com/paper/2512.10382/) (2025) - [Time-Unconditional Generative Speech Enhancement via Autonomous Rectified Flow](https://mlsanity.com/paper/2606.20001/) (2026) - [Speech Enhancement based on cascaded two flows](https://mlsanity.com/paper/2508.06842/) (2025) - [Dual-View Predictive Diffusion: Lightweight Speech Enhancement via Spectrogram-Image Synergy](https://mlsanity.com/paper/2602.00568/) (2026) - [A Fast Solver for Interpolating Stochastic Differential Equation Diffusion Models for Speech Restoration](https://mlsanity.com/paper/2603.09508/) (2026) - [SB-RF: Schr"odinger Bridge Rectified Flow for One-Step Robust Speech Enhancement](https://mlsanity.com/paper/2606.05575/) (2026) - [Beyond U-Net: A Latent-Representation-Aligned Skip-Free Backbone for Flow-Matching Speech Enhancement](https://mlsanity.com/paper/2606.24745/) (2026) ## Abstract (arXiv) 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.