The strong performance that modern semantic correspondence methods achieve at standard thresholds plateaus sharply at fine-grained thresholds. We argue that this plateau stems not from the representational capacity of backbone features, but from a grid-tied readout. Patch-based vision transformers tokenize images onto discrete grids, introducing two forms of quantization error: querying nearest patch features instead of exact keypoints on the source side, and the absence of grid features representing precise ground-truth locations on the target side. We quantify this quantization ceiling across all 499,188 keypoints in SPair-71k: under the standard 448x448, patch-14 setting, 84.9% of ground-truth keypoints have no grid feature representing their precise location at [email protected]. This is a structural limitation at the representation level, independent of the matching strategy. We address this with ImCorr: Sub-pixel Semantic Correspondence via Implicit Feature Decoding, which formulates correspondence estimation over a continuous feature field queryable at arbitrary continuous coordinates. A FiLM-conditioned decoder is trained to embed sub-pixel positional information into the feature field. Querying the field directly at exact keypoint coordinates theoretically eliminates representation-level quantization error on the source side, while decoding onto a grid denser than the backbone grid substantially reduces quantization error on the target side. On SPair-71k and AP-10K (intra-species, cross-species, and cross-family), ImCorr improves performance at fine-grained thresholds ([email protected]), achieving a 6.2 percentage point gain over the prior state of the art at [email protected] on SPair-71k. These results demonstrate that representational continuity is an effective solution for precise semantic correspondence. Code is available at https://github.com/YusungChoi/ImCorr.

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