Functional magnetic resonance imaging (fMRI) utilizes echo-planar imaging (EPI) to capture blood-oxygen-level-dependent (BOLD) signals with high temporal resolution. However, EPI is inherently sensitive to magnetic field inhomogeneities, resulting in susceptibility-induced geometric distortions along the phase-encoding (PE) direction. To correct these distortions, conventional approaches rely on additional calibration scans, such as field maps or reverse PE acquisitions, which are not always available in practice. To overcome this limitation, we propose SACRED, a calibration scan-free susceptibility distortion correction framework that corrects geometric distortions via image translation-based registration using only a routinely acquired anatomical T1-weighted (T1w) image and a unidirectional PE BOLD image. SACRED employs an invertible neural network as the image translation backbone to bridge the contrast gap between BOLD and T1w images while enforcing structural consistency through a modality independent neighborhood descriptor. This design enables the use of a mono-contrast similarity objective to train the registration network in an unsupervised manner without requiring distortion-corrected BOLD images. In addition, we incorporate test-time adaptation (TTA) to further enhance performance on out-of-distribution (OOD) data at inference time. SACRED was evaluated on one in-distribution (ID) dataset and two OOD datasets, and was compared with representative fMRI distortion correction methods. The results demonstrate that SACRED significantly outperforms competing methods on both ID and OOD datasets, exhibiting robustness to scanner and population shifts, partly enabled by TTA. The code will be made publicly available upon acceptance.

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