Image-to-image translation models have achieved notable success in converting images across visual domains and are increasingly used for medical tasks such as predicting post-operative outcomes and modeling disease progression. However, most existing methods primarily aim to match the target distribution and often neglect spatial correspondences between the source and translated images. This limitation can lead to structural inconsistencies and hallucinations, undermining the reliability and interpretability of the predictions. These challenges are accentuated in clinical applications by the stringent requirement for anatomical accuracy. In this work, we present TraceTrans, a novel deformable image translation model designed for post-operative prediction that generates images aligned with the target distribution while explicitly revealing spatial correspondences with the pre-operative input. The framework employs an encoder for feature extraction and dual decoders for predicting spatial deformations and synthesizing the translated image. The predicted deformation field imposes spatial constraints on the generated output, ensuring anatomical consistency with the source. Extensive experiments on medical cosmetology and brain MRI datasets demonstrate that TraceTrans delivers accurate and interpretable post-operative predictions, highlighting its potential for reliable clinical deployment.