Abstract
In this paper, we propose a variance-preserving interpolation framework to improve diffusion models for single-channel speech enhancement (SE) and automatic speech recognition (ASR). This new variance-preserving interpolation diffusion model (VPIDM) approach requires only 25 iterative steps and obviates the need for a corrector, an essential element in the existing variance-exploding interpolation diffusion model (VEIDM). Two notable distinctions between VPIDM and VEIDM are the scaling function of the mean of state variables and the constraint imposed on the variance relative to the mean's scale. We conduct a systematic exploration of the theoretical mechanism underlying VPIDM and develop insights regarding VPIDM's applications in SE and ASR using VPIDM as a frontend. Our proposed approach, evaluated on two distinct data sets, demonstrates VPIDM's superior performances over conventional discriminative SE algorithms. Furthermore, we assess the performance of the proposed model under var