Medical image re-identification (MedReID) enables longitudinal patient linkage but remains vulnerable to shortcut learning and often produces decisions that clinicians cannot audit against named anatomy. We propose Graph-of-Differences (GoD), which grounds identity comparisons in explicit anatomical structure. Each image is represented as an anatomy graph whose nodes correspond to named anatomical regions; given an image pair, soft node correspondence is established, and differences are computed over matched anatomy. A graph-level difference alignment objective ties these anatomy-matched differences to the global backbone difference, ensuring the retrieval signal is anchored in homologous structures rather than arbitrary spatial tokens. Explanations are defined over named graph nodes and quantitatively audited via node insertion/deletion tests, replacing unstable pixel heatmaps with verifiable structure-level evidence. On internal benchmarks, GoD improves Rank-1 by +7.1 pp on fundus and +3.1 pp on CXR over a strong frozen-backbone baseline, with further gains on zero-shot external transfers confirming that anatomy grounding improves both accuracy and generalization. Code is available at https://github.com/GenMI-Lab/GoD.git.

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