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.
@article{arxiv.2603.09508,
title = {A Fast Solver for Interpolating Stochastic Differential Equation Diffusion Models for Speech Restoration},
author = {Bunlong Lay and Timo Gerkmann},
journal= {arXiv preprint arXiv:2603.09508},
year = {2026}
}