Magnetic Resonance Unpaired Image Translation with Pseudometric Schrödinger Bridges

Unpaired image translation is a critical preprocessing strategy for synthesizing missing sequences and harmonizing contrast variability in magnetic resonance (MR) imaging. However, in medical image processing, distribution-level translation is insufficient; it is vitally important that the anatomy is not distorted, corrupted, or lost after translation. Previous methods, like diffusion Schrödinger bridge matching (DSBM) achieve image translation, but do not preserve anatomy. We introduce the pseudometric Schrödinger bridge (PMSB), which trains two independent volume-preserving, isometry-regularized diffeomorphisms to map data from each domain to a latent anatomic pseudometric space. Then, DSBM is used within that space, explicitly minimizing the transport gap while preserving anatomy. Extensive experiments on the multi-contrast OASIS-3 dataset demonstrate that PMSB establishes a new state-of-the-art in structural consistency for cross-contrast synthesis. PMSB outperforms other leading methods and drastically reduces anatomical hallucinations, notably yielding a mean PSNR of 26.70 dB, a mean SSIM of 0.86, and a mean LNCC of 0.24.