Scene graphs provide structured abstractions for scene understanding, yet they often overfit to spurious correlations, severely hindering out-of-distribution generalization. To address this limitation, we propose CURVE, a causality-inspired framework that integrates variational uncertainty modeling with uncertainty-guided structural regularization to suppress high-variance, environment-specific relations. Specifically, we apply prototype-conditioned debiasing to disentangle invariant interaction dynamics from environment-dependent variations, promoting a sparse and domain-stable topology. Empirically, we evaluate CURVE in zero-shot transfer and low-data sim-to-real adaptation, verifying its ability to learn domain-stable sparse topologies and provide reliable uncertainty estimates to support risk prediction under distribution shifts.