Network-wide traffic volume estimation typically relies on propagating measurements from fixed sensors, making performance highly dependent on sensor density and limiting deployment in sparsely instrumented networks. We propose a link-level learning framework that estimates hourly traffic volumes from widely available territorial data only, including probe speed profiles, road and topological descriptors, along with weather observations. A supervised local mapping is learned from sparse sensor measurements and evaluated under two generalization settings: intra-network (unseen links within the training network) and inter-network (unseen city). This formulation frames traffic volume estimation as a spatial out-of-distribution generalization problem under sparse supervision. To enhance spatial robustness, we introduce a capacity-aware formulation that models volume as the product of a link-specific structural capacity and an hourly regime-aware utilization ratio, embedding traffic-theoretic constraints directly into the learning process. Extensive experiments in both generalization settings demonstrate that the proposed structural constraints consistently outperform a state-of-the-art baseline under spatial distribution shift.

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