Structure Lives in the Representation: Phase-Field Diffusion for Robust ECG Delineation

Under noise, the masks of neural ECG delineators fragment and misorder, breaking the $P\to QRS\to T$ sequence that interval measurement presupposes. Point-level F1, the standard metric, overstates the usable fiducials. The standard remedy, rule-based post-processing, reassembles detected waves but cannot synthesize missed ones. We replace repair with generation and move structure into the learning target. We train a conditional diffusion prior over phase fields: each wave class occupies a channel whose value tracks within-wave phase. The target is continuous and invertible, encoding presence, boundaries, and order, not enforcing them afterwards. The conventional one-hot, a flat label with no within-wave position, is structurally fragile. Under the harshest external-test noise, even trained with the field's own loss, it reaches rules only by selecting among samples. Its single draw reads 0.794 against rules' 0.863. Averaging them collapses at the decision-boundary readout of established conventions. The phase field needs no such crutch. A single draw lands in rules' seed band, clearing rules at the reported pairing (0.888); its gain over the matched one-hot is positive at every seed. The same selection lifts harshest-condition legality to 0.994, above the one-hot's 0.980, and averaging stays legal without decode tuning. Legality is not bought by deleting waves: the field misses fewer ground-truth P waves than rules, attains the best F1, and trails rules on intervals by milliseconds. Under the harshest noise, generation replaces rule repair; structure steers generation.