Establishing dense, robust image correspondences under large-scale variations, perspective distortions, and occlusions remains a core challenge in computer vision. We introduce PIXELMAP, a swarm-inspired framework that refines local affine transformations in a structured Affine Correspondence Grid (AC-Grid) while ensuring global consistency through Iterative Refinement (IR). Each grid cell acts as an autonomous "agent," adapting its transformation based on a Correspondence Mapping (CM) mechanism that propagates improvements among neighbors. This localized agent-based approach naturally supports massive parallelization and achieves state-of-the-art accuracy across diverse imaging conditions-without requiring training data. Extensive experiments on synthetic distortions and real-world images demonstrate that PIXELMAP maintains high precision and recall, even under severe geometric distortions and noise. An open-source implementation and interactive website further facilitate adoption and invite contributions to this scalable, training-free solution for dense correspondence (GitHub, Interactive Website).