# HybridSB-MoE: Dual-Domain Schr"odinger Bridges with Scene-Adaptive Expert Routing for Speech Enhancement

arXiv: https://arxiv.org/abs/2608.12715 · HTML: https://mlsanity.com/paper/2608.12715/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Multimodal MoE models, one of 12 directions in Mixture-of-experts.
- Builds on 43 of its 54 references that are in the map.
- First posted on arXiv 13 Aug 2026.

## Placed in

- Mixture-of-experts / [Multimodal MoE models](https://mlsanity.com/moe/multimodal-moe-models/)

## Builds on (most cited first, 30 of 43)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [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)
- [Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theory](https://mlsanity.com/paper/2110.11291/) (2021)
- [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)
- [Real Time Speech Enhancement in the Waveform Domain](https://mlsanity.com/paper/2006.12847/) (2020)
- [Dual-path RNN: efficient long sequence modeling for time-domain single-channel speech separation](https://mlsanity.com/paper/1910.06379/) (2019)
- [SEGAN: Speech Enhancement Generative Adversarial Network](https://mlsanity.com/paper/1703.09452/) (2017)
- [Diffusion Schr"odinger Bridge Matching](https://mlsanity.com/paper/2303.16852/) (2023)
- [Speech Enhancement with Score-Based Generative Models in the Complex STFT Domain](https://mlsanity.com/paper/2203.17004/) (2022)
- [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)
- [FullSubNet+: Channel Attention FullSubNet with Complex Spectrograms for Speech Enhancement](https://mlsanity.com/paper/2203.12188/) (2022)

## Abstract (arXiv)

Generative speech enhancement faces three gaps: spectral models capture harmonic structure but often disrupt phase, waveform models preserve phase but miss harmonics, and Schr"odinger Bridges (SB) shorten transport from noise to clean speech but leave inference cost only loosely tied to training. We propose HybridSB-MoE, a dual-domain framework that fills these gaps through three contributions unified by a single asymmetric design principle. (i) Asymmetric uncertainty fusion: The spectral path captures epistemic uncertainty via expert disagreement, while the waveform bridge models aleatoric variance through stochastic dynamics. We fuse them asymmetrically, allowing the mixing weight to adapt to distinct error regimes rather than average predictions. (ii) Heterogeneous MoE with top-k=2 routing across five distinct architectural archetypes, where architectural diversity makes the epistemic signal indicate which inductive bias fails rather than small perturbations among similar experts. (iii) Discretization bound (Theorem 1): path-consistency and trajectory regularizers together bound the K-step bridge sampling error in 2-Wasserstein distance at rate K-alpha, making small-K inference an objective-level guarantee rather than an empirical claim. On VoiceBank+DEMAND, HybridSB-MoE outperforms diffusion- and SB-based baselines at their step budgets while remaining competitive with consistency-distilled few-step methods.