Barrett’s esophagus (BE) is a precursor to esophageal adenocarcinoma (EAC), a highly lethal malignancy when detected late but treatable in its early stages. Surveillance programs are designed to identify neoplastic changes early, but the extremely low prevalence of neoplasia (<1%) poses major challenges for both clinical detection and the development of reliable computer-aided detection and diagnosis (CADe/x) systems. In such low-prevalence settings, developing traditional supervised machine learning models is challenging, often requiring artificially balanced datasets that do not reflect real-world deployment conditions, leading to limited generalization. In contrast, we propose reframing BE neoplasia detection as an out-of-distribution (OOD) problem, training generative models exclusively on healthy (non-dysplastic) images to identify rare pathological deviations. We systematically evaluate the trade-offs between supervised and generative approaches under varying prevalence and data regimes, and find that generative models offer a promising, prevalence-agnostic alternative in low-prevalence settings, although they still face limitations in sensitivity to subtle lesions. This study demonstrates the potential of generative OOD modeling as a prevalence-independent alternative for rare-event detection in BE surveillance settings, with broader implications for other low-prevalence domains in medical imaging and early cancer detection in general.