Pathology foundation models (PFMs) provide strong tissue representations and have become central to digital pathology. However, deployment in disease-specific settings is limited by 1) the high computational cost of billion-parameter PFMs and 2) distribution mismatch and non-biological bias inherited from pan-cancer, multi-centre pre-training, including site-specific signatures and imbalanced disease prevalence. These factors can encourage shortcut learning and under-emphasise subtle morphology required for reliable modelling of a specific cancer type. We present SmartStu (a Smart Student), a framework to customise compact, breast-cancer-specific PFMs via distillation whilst mitigating confounding. SmartStu distils representations from multiple teacher PFMs into a lightweight student backbone. Crucially, we introduce adversarial distillation that leverages a dedicated noise model trained to predict nuisance, edge-dominated cues on the distillation set. Using this noise model as a counterexample, the adversarial objective encourages the student to recognise, yet suppress, features predictive of nuisance targets. We further incorporate multi-teacher ensemble distillation and an auxiliary self-supervised objective with artefact injection. We validate SmartStu on three external cohorts (Yale HER2, SLN-Breast, and BRACS) with multiple tiny backbones. SmartStu yields breast-cancer-specific PFMs that are over $30\times$ smaller than general PFMs whilst largely preserving, and sometimes improving, downstream performance measured by balanced accuracy (bAcc) and AUC. Code is available at https://github.com/zwchen03/advDistall.

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