Visual classifiers are expected to generalize under data shifts, target shifts, and their combinations, yet most existing methods focus on domain invariance while failing to address intra-image predictive sufficiency. We investigate the structural hypothesis that each image contains a sample-adaptive oracle intra-image predictive subset sufficient for label prediction, while the remaining patches form non-essential complementary context that may correlate with the label. The theoretical analysis shows that restricting prediction to this oracle subset preserves the Bayes risk achievable by the full-patch representation while admitting a complexity bound that tightens with the oracle-subset size. Based on this view, we propose PatchGen, a text-free module that learns a sample-dependent soft predictive-subset mask as a task-driven proxy for the unobserved oracle subset mask. Specifically, histopathology visualizations suggest that PatchGen assigns higher scores to tumor-consistent regions than to some frequently co-occurring inflammatory context. Extensive experiments on natural and histopathological image benchmarks spanning all three shift settings show that PatchGen improves average performance over matched-backbone baselines in most evaluated configurations, enhances generalization to unknown classes, and remains competitive with vision-language methods without text supervision.