Dense self-supervised learning (SSL) methods showed its effectiveness in enhancing the fine-grained semantic understandings of vision models. However, existing approaches often rely on parametric assumptions or complex post-processing (e.g., clustering, sorting), limiting their flexibility and stability. To overcome these limitations, we introduce Patch-level Kernel Alignment (PaKA), a non-parametric, kernel-based approach that improves the dense representations of pretrained vision encoders with a post-(pre)training. Our method propose a robust and effective alignment objective that captures statistical dependencies which matches the intrinsic structure of high-dimensional dense feature distributions. In addition, we revisit the augmentation strategies inherited from image-level SSL and propose a refined augmentation strategy for dense SSL. Our framework improves dense representations by conducting a lightweight post-training stage on top of a pretrained model. With only 14 hours of additional training on a single GPU, our method achieves state-of-the-art performance across a range of dense vision benchmarks, demonstrating both efficiency and effectiveness.