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In the era of large-scale foundation models, fully fine-tuning pretrained networks for each downstream task is often prohibitively resource-intensive. Prompt tuning offers a lightweight alternative by introducing tunable prompts while keeping the backbone frozen. However, existing visual prompt tuning methods often fail to specialize the prompts or enrich the representation space--especially when applied to self-supervised backbones. We show that these limitations become especially pronounced in challenging tasks and data-scarce settings, where effective adaptation is most critical. In this work, we introduce VIPAMIN, a visual prompt initialization strategy that enhances adaptation of self-supervised models by (1) aligning prompts with semantically informative regions in the embedding space, and (2) injecting novel representational directions beyond the pretrained subspace. Despite its simplicity--requiring only a single forward pass and lightweight operations--VIPAMIN consistently improves performance across diverse tasks and dataset sizes, setting a new state of the art in visual prompt tuning.