Dense correspondence matching has historically been bounded by simplifying spatio-temporal priors, such as smooth motion and rigid geometry. While effective for classical tasks, these assumptions break down in image editing and reference-guided generation (IEG), where transformations can preserve visual identity while breaking physical continuity. To establish identity-preserving correspondence across such transformations, we introduce FreeMatching, a generalizable framework combining generative and semantic foundation representations with heterogeneous supervision from classical datasets, tracked videos, and synthetic scenes. Teacher-guided iterative refinement further improves correspondence in IEG without dense correspondence annotations. Experimentally, a single FreeMatching model substantially improves correspondence quality on challenging IEG image pairs while retaining competitive performance on classical benchmarks. Furthermore, we demonstrate its utility as a quantitative metric for evaluating identity preservation, with scores that correlate with human judgment. The code is available at https://github.com/luping-liu/FreeMatching.

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