Frequency-Dependent Scheduled Schrödinger Bridge for Underwater Acoustic Signal Denoising

Abstract Schrödinger Bridge-based diffusion models have demonstrated promising performance in signal denoising. However, since ground truth signals are unavailable during the sampling process, neural networks must be employed to learn the mapping, which breaks the theoretical coupling between diffusion and sampling processes. This paper reveals a critical inconsistency between the theoretical diffusion path and the learned sampling trajectory across different frequency bands. This diffusion-sampling inconsistency directly undermines denoising effectiveness. To address this limitation, we propose the Frequency-Dependent Scheduled Schrödinger Bridge (FDSSB), which leverages power spectral density to adaptively schedule diffusion processes across frequencies. This mechanism assigns asynchronous diffusion schedules to different frequency components, correcting the diffusion schedule to better match the sampling process. As a result, FDSSB effectively mitigates the mismatch and enhances the consistency between diffusion and sampling processes. Extensive experiments demonstrate that FDSSB achieves state-of-the-art performance, with an average scale-invariant signal-to-noise ratio improvement of 7.9066 dB over competitive approaches.