# A Fast Solver for Interpolating Stochastic Differential Equation Diffusion Models for Speech Restoration

arXiv: https://arxiv.org/abs/2603.09508 · HTML: https://mlsanity.com/paper/2603.09508/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 28 of its 42 references that are in the map.
- First posted on arXiv 10 Mar 2026.

## Placed in

- Diffusion models / [Audio, speech and music](https://mlsanity.com/diffusion/audio-speech-and-music/)

## Builds on (most cited first, 28 of 28)

- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (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)
- [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)
- [DPM-Solver-v3: Improved Diffusion ODE Solver with Empirical Model Statistics](https://mlsanity.com/paper/2310.13268/) (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)
- [Speech Enhancement with Score-Based Generative Models in the Complex STFT Domain](https://mlsanity.com/paper/2203.17004/) (2022)
- [The Principles of Diffusion Models](https://mlsanity.com/paper/2510.21890/) (2025)
- [EARS: An Anechoic Fullband Speech Dataset Benchmarked for Speech Enhancement and Dereverberation](https://mlsanity.com/paper/2406.06185/) (2024)
- [A Study on Speech Enhancement Based on Diffusion Probabilistic Model](https://mlsanity.com/paper/2107.11876/) (2021)
- [Reducing the Prior Mismatch of Stochastic Differential Equations for Diffusion-based Speech Enhancement](https://mlsanity.com/paper/2302.14748/) (2023)
- [Schr"odinger Bridge for Generative Speech Enhancement](https://mlsanity.com/paper/2407.16074/) (2024)
- [Investigating Training Objectives for Generative Speech Enhancement](https://mlsanity.com/paper/2409.10753/) (2024)
- [FlowDec: A flow-based full-band general audio codec with high perceptual quality](https://mlsanity.com/paper/2503.01485/) (2025)
- [Distillation and Pruning for Scalable Self-Supervised Representation-Based Speech Quality Assessment](https://mlsanity.com/paper/2502.05356/) (2025)
- [SE-Bridge: Speech Enhancement with Consistent Brownian Bridge](https://mlsanity.com/paper/2305.13796/) (2023)
- [Thunder : Unified Regression-Diffusion Speech Enhancement with a Single Reverse Step using Brownian Bridge](https://mlsanity.com/paper/2406.06139/) (2024)
- [Few-step Adversarial Schr"odinger Bridge for Generative Speech Enhancement](https://mlsanity.com/paper/2506.01460/) (2025)
- [Diffusion Buffer: Online Diffusion-based Speech Enhancement with Sub-Second Latency](https://mlsanity.com/paper/2506.02908/) (2025)
- [Variance-Preserving-Based Interpolation Diffusion Models for Speech Enhancement](https://mlsanity.com/paper/2306.08527/) (2023)

## Abstract (arXiv)

Diffusion Probabilistic Models (DPMs) are a well-established class of diffusion models for unconditional image generation, while SGMSE+ is a well-established conditional diffusion model for speech enhancement. One of the downsides of diffusion models is that solving the reverse process requires many evaluations of a large Neural Network. Although advanced fast sampling solvers have been developed for DPMs, they are not directly applicable to models such as SGMSE+ due to differences in their diffusion processes. Specifically, DPMs transform between the data distribution and a standard Gaussian distribution, whereas SGMSE+ interpolates between the target distribution and a noisy observation. This work first develops a formalism of interpolating Stochastic Differential Equations (iSDEs) that includes SGMSE+, and second proposes a solver for iSDEs. The proposed solver enables fast sampling with as few as 10 Neural Network evaluations across multiple speech restoration tasks.