# Regularized Schr"odinger Bridge via Distortion-Perception Perturbation for High-Fidelity Speech Enhancement

arXiv: https://arxiv.org/abs/2511.11686 · HTML: https://mlsanity.com/paper/2511.11686/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 52 references that are in the map.
- First posted on arXiv 12 Nov 2025.

## Builds on (most cited first, 30 of 39)

- [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)
- [Robust Speech Recognition via Large-Scale Weak Supervision](https://mlsanity.com/paper/2212.04356/) (2022)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [SDR - half-baked or well done?](https://mlsanity.com/paper/1811.02508/) (2018)
- [UTMOS: UTokyo-SaruLab System for VoiceMOS Challenge 2022](https://mlsanity.com/paper/2204.02152/) (2022)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Deblurring via Stochastic Refinement](https://mlsanity.com/paper/2112.02475/) (2021)
- [DNSMOS: A Non-Intrusive Perceptual Objective Speech Quality metric to evaluate Noise Suppressors](https://mlsanity.com/paper/2010.15258/) (2020)
- [Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theory](https://mlsanity.com/paper/2110.11291/) (2021)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (2023)
- [Speech Enhancement and Dereverberation with Diffusion-based Generative Models](https://mlsanity.com/paper/2208.05830/) (2022)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [WHAM!: Extending Speech Separation to Noisy Environments](https://mlsanity.com/paper/1907.01160/) (2019)
- [Conditional Diffusion Probabilistic Model for Speech Enhancement](https://mlsanity.com/paper/2202.05256/) (2022)
- [MetricGAN+: An Improved Version of MetricGAN for Speech Enhancement](https://mlsanity.com/paper/2104.03538/) (2021)
- [StoRM: A Diffusion-based Stochastic Regeneration Model for Speech Enhancement and Dereverberation](https://mlsanity.com/paper/2212.11851/) (2022)
- [Speech Enhancement with Score-Based Generative Models in the Complex STFT Domain](https://mlsanity.com/paper/2203.17004/) (2022)
- [Elucidating the Exposure Bias in Diffusion Models](https://mlsanity.com/paper/2308.15321/) (2023)
- [Input Perturbation Reduces Exposure Bias in Diffusion Models](https://mlsanity.com/paper/2301.11706/) (2023)
- [Alleviating Exposure Bias in Diffusion Models through Sampling with Shifted Time Steps](https://mlsanity.com/paper/2305.15583/) (2023)
- [TF-GridNet: Integrating Full- and Sub-Band Modeling for Speech Separation](https://mlsanity.com/paper/2211.12433/) (2022)
- [An Investigation of Incorporating Mamba for Speech Enhancement](https://mlsanity.com/paper/2405.06573/) (2024)
- [A Study on Speech Enhancement Based on Diffusion Probabilistic Model](https://mlsanity.com/paper/2107.11876/) (2021)
- [A Theory of the Distortion-Perception Tradeoff in Wasserstein Space](https://mlsanity.com/paper/2107.02555/) (2021)
- [Analysing Diffusion-based Generative Approaches versus Discriminative Approaches for Speech Restoration](https://mlsanity.com/paper/2211.02397/) (2022)
- [Posterior-Mean Rectified Flow: Towards Minimum MSE Photo-Realistic Image Restoration](https://mlsanity.com/paper/2410.00418/) (2024)
- [Schrodinger Bridges Beat Diffusion Models on Text-to-Speech Synthesis](https://mlsanity.com/paper/2312.03491/) (2023)
- [Schr"odinger Bridge for Generative Speech Enhancement](https://mlsanity.com/paper/2407.16074/) (2024)

## Built on by (most cited first, 1 of 1)

- [Corrective Forcing: Unified Post-Training for Diffusions and Flows in Generative Speech Enhancement](https://mlsanity.com/paper/2609.24651/) (2026)

## Abstract (arXiv)

Speech enhancement (SE) requires high-fidelity reconstruction of clean speech that preserves linguistic and paralinguistic cues while maintaining high perceptual quality. Recently, Schr"odinger Bridge (SB), a family of diffusion-based generative models, has advanced SE by bridging degraded and clean speech distributions in a principled formulation, enabling higher-quality reconstructions with fewer sampling steps. However, diffusion-based SE methods still face two challenges: (1) the fidelity-realism tradeoff, where they often prioritize perceptual realism encouraged by the learned speech prior, at the expense of fidelity; and (2) the exposure bias issue, where iterative multi-step sampling causes early-step prediction errors to accumulate along the sampling trajectory and degrade enhanced speech quality. In this paper, we analyze standard SB training and show that it induces a systematic prediction drift, which biases the multi-step trajectory and amplifies error accumulation. To address this, we propose Regularized Schr"odinger Bridge (RSB) for high-fidelity SE, a generative approach that reconciles fidelity and realism while mitigating exposure bias. RSB regularizes training with a Distortion-Perception Perturbation that constructs time-varying targets by interpolating between clean speech and posterior-mean estimates, and trains the network on perturbed intermediate states to correct toward the ground truth progressively. By simulating inference-time prediction errors, this perturbation mitigates the training-inference mismatch and thereby alleviates exposure bias. It also injects posterior-mean estimates as fidelity-preserving guidance, thereby improving reconstruction fidelity.