Regularized Schrödinger Bridge: Alleviating Distortion and Exposure Bias in Solving Inverse Problems

Diffusion models serve as a powerful generative framework for solving inverse problems. However, they still face two key challenges: 1) the distortion-perception tradeoff, where improving perceptual quality often degrades reconstruction fidelity, and 2) the exposure bias problem, where the training-inference input mismatch leads to prediction error accumulation and reduced reconstruction quality. In this work, we propose the Regularized Schrödinger Bridge (RSB), an adaptation of Schrödinger Bridge tailored for inverse problems that addresses the above limitations. RSB employs a novel regularized training strategy that perturbs both the input states and targets, effectively mitigating exposure bias by exposing the model to simulated prediction errors and also alleviating distortion by well-designed interpolation via the posterior mean. Extensive experiments on two typical inverse problems for speech enhancement demonstrate that RSB outperforms state-of-the-art methods, significantly improving distortion metrics and effectively reducing exposure bias.