GO-Flow: Positive-Only Graph Learning from Conditional Flow Fields

In many graph prediction problems, the observed positives are reliable, whereas the unobserved graph objects are ambiguous: a missing edge may be an undiscovered relation, and an unlabeled node may still belong to the target class. We study positive-only graph learning, where trainable parameters are fit from observed positives without assigning negative labels to the remaining graph objects or using them as unlabeled training examples. Conditional flow matching provides a positive-density model, but density estimation alone does not determine how candidates should be ranked. We introduce GO-Flow (Graph learning from Observed positives with conditional Flow), which fits a conditional flow only on observed positive graph objects and uses it to score the unlabeled candidates; for relations, the score contrasts conditional and background densities so that it reflects what the candidate context adds. Relation prediction is the primary instantiation, evaluated across standard link prediction and drug-target interaction, while node positive-unlabeled ranking and a class-as-positive study apply the same conditional flow to nodes. With positive-only training and per-dataset selection, which uses sampled validation non-edges, GO-Flow improves over the learned one-class baselines on all eight link-prediction datasets and compares favorably with the positive-only baselines on seven; methods that additionally use unlabeled or negative examples remain stronger in some regimes, since the unlabeled pool and reliable negative labels carry information that positives alone do not, whereas hidden positives labeled negative degrade these methods.