Speech enhancement (SE) requires high-fidelity reconstruction of clean speech that preserves linguistic and paralinguistic cues while maintaining high perceptual quality. Recently, Schrödinger Bridge (SB), a family of diffusion-based generative models, has advanced SE by bridging degraded and clean speech distributions in a principled formulation, enabling higher-quality reconstructions with fewer sampling steps. However, diffusion-based SE methods still face two challenges: (1) the fidelity-realism tradeoff, where they often prioritize perceptual realism encouraged by the learned speech prior, at the expense of fidelity; and (2) the exposure bias issue, where iterative multi-step sampling causes early-step prediction errors to accumulate along the sampling trajectory and degrade enhanced speech quality. In this paper, we analyze standard SB training and show that it induces a systematic prediction drift, which biases the multi-step trajectory and amplifies error accumulation. To address this, we propose Regularized Schrödinger Bridge (RSB) for high-fidelity SE, a generative approach that reconciles fidelity and realism while mitigating exposure bias. RSB regularizes training with a Distortion-Perception Perturbation that constructs time-varying targets by interpolating between clean speech and posterior-mean estimates, and trains the network on perturbed intermediate states to correct toward the ground truth progressively. By simulating inference-time prediction errors, this perturbation mitigates the training-inference mismatch and thereby alleviates exposure bias. It also injects posterior-mean estimates as fidelity-preserving guidance, thereby improving reconstruction fidelity.

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