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

2025-11-12

AI Summary

Diffusion models for inverse problems face two key challenges: the distortion–perception trade-off and exposure bias. To address these, we propose Regularized Schrödinger Bridge (RSB), a novel framework that jointly perturbs both observations and target variables, introduces a posterior-mean interpolation path, and explicitly models cumulative prediction error during training. Theoretically, RSB unifies forward diffusion and reverse inference under coupled constraints derived from optimal transport. Practically, it achieves superior balance between reconstruction fidelity and perceptual quality. Evaluated on speech enhancement, RSB significantly reduces objective distortion metrics (e.g., PESQ and WER) while improving subjective listening scores—outperforming state-of-the-art diffusion-based baselines and conventional supervised methods. These results demonstrate RSB’s robustness and generalization capability across diverse degradation scenarios.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Learning to Search
• Machine Learning: Adversarial Learning & Robustness

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

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.

Problem

• Addresses distortion-perception tradeoff in inverse problems
• Mitigates exposure bias from training-inference mismatch
• Improves reconstruction fidelity in diffusion model applications

Innovation

• Regularized Schrödinger Bridge for inverse problems
• Perturbs input states and targets to reduce exposure bias
• Uses posterior mean interpolation to alleviate distortion