Learning Shared Bidirectional Latent Dynamics for Translation Between CT and MRI

Bidirectional image translation is an important problem in computer vision because many related visual domains require mappings in both directions. A representative case is translation between CT and MRI, which provide complementary anatomical and tissue information but may not always be simultaneously available. Existing methods commonly train separate models for translation from CT to MRI and from MRI to CT, treating the two directions as independent tasks and leaving their shared structure insufficiently explored. To address this limitation, we formulate the two translation directions as latent state evolution processes governed by shared dynamics. Modality specific VAEs encode CT and MRI into latent representations, and a shared velocity model transports the source representation toward the target. Since the same dynamics model must represent two different translation directions, we introduce latent anchors that combine the source state with direction information and guide velocity prediction. The anchor is used as a reference during latent evolution rather than as the predicted target itself. An image space refiner further corrects residual errors after decoding. Experiments on two public paired CT and MRI datasets demonstrate consistent performance across both translation directions and MRI contrasts, with the proposed framework achieving the highest mean PSNR and SSIM among the compared methods. Ablation studies further show that direct parameter sharing introduces a performance gap, while explicit direction modeling, particularly the proposed anchor formulation, largely recovers this loss. Source code is provided in the supplementary material.