Feasible Flow Matching for Graph Reconstruction via Within-Sampling Primal-Dual Guidance
Haoming Chen, Nicolas Zilberstein, Santiago Paternain, Santiago Segarra
Abstract
Graph reconstruction from partial observations often comes with structural side information, such as degree bounds, triangle counts, or an edge-density band. Prior-Informed Flow Matching (PIFM) reconstructs graphs by transporting a local prior toward the graph distribution, but it provides no mechanism to incorporate this side information. We put forth Constrained Primal-Dual PIFM (CPD-PIFM), which augments the sampler with Lagrange multipliers that evolve along each trajectory. The multipliers respond to constraint violations at a predicted endpoint and guide subsequent sampling steps without retraining. We prove that the sampler inherits PIFM's permutation equivariance and bound its expected terminal slack by a term that decays as the inverse square root of the number of steps, plus two approximation terms. On three link-prediction benchmarks and nine combinations of datasets and constraints, CPD-PIFM raises feasibility by 11-26 percentage points and remains competitive with fixed guidance without selecting a separate multiplier for each constraint.