Bridge-SR: Schr\"odinger Bridge for Efficient SR

Speech super-resolution (SR), which generates a waveform at a higher sampling rate from its low-resolution version, is a long-standing critical task in speech restoration. Previous works have explored speech SR in different data spaces, but these methods either require additional compression networks or exhibit limited synthesis quality and inference speed. Motivated by recent advances in probabilistic generative models, we present Bridge-SR, a novel and efficient any-to-48kHz SR system in the speech waveform domain. Using tractable Schr\"odinger Bridge models, we leverage the observed low-resolution waveform as a prior, which is intrinsically informative for the high-resolution target. By optimizing a lightweight network to learn the score functions from the prior to the target, we achieve efficient waveform SR through a data-to-data generation process that fully exploits the instructive content contained in the low-resolution observation. Furthermore, we identify the importance of the noise schedule, data scaling, and auxiliary loss functions, which further improve the SR quality of bridge-based systems. The experiments conducted on the benchmark dataset VCTK demonstrate the efficiency of our system: (1) in terms of sample quality, Bridge-SR outperforms several strong baseline methods under different SR settings, using a lightweight network backbone (1.7M); (2) in terms of inference speed, our 4-step synthesis achieves better performance than the 8-step conditional diffusion counterpart (LSD: 0.911 vs 0.927). Demo at https://bridge-sr.github.io.