The multi-scan imaging procedure, involving both multi-modal and multi-timepoint scans, captures temporal changes and complementary cross-modality information, playing a key role in clinical diagnosis. Multi-scan image restoration (IR), which leverages high-quality reference scans to aid in restoring degraded current scans, holds significant potential for reducing the cost of the multi-scan procedure. However, misalignment between scans, arising from patient physiological or posture changes, impacts the ability of networks to exploit cross-scan correlations and leads to declined restoration performance. To this end, we propose a plug-and-play Bridge-Based Module for Misalignment Estimation and Elimination (BME \(^2\) ), which adopts a coarse-to-fine strategy to estimate cross-scan misalignment. Specifically, a lightweight misalignment estimation (ME) network first predicts the initial deformation fields, which are then iteratively refined via a latent Schr \(\ddot{\textrm{o}}\) dinger bridge-based model to obtain the final estimation. Notably, BME \(^2\) can be added to arbitrary backbones and only introduces mild computational costs. Validated on brain MRI and abdominal CT datasets, BME \(^2\) universally enhances four baselines, achieving average PSNR gains of 0.54 and 0.65 dB on brain and abdominal data, respectively. The codes are available at: https://github.com/ChenWenxuan2021/BME2 .