Scene graph generation takes a camera image and derives a graph representation of key objects in the image and their relations. This core computer vision task is often used in autonomous driving, where traditional software and machine learning (ML) components are used in tandem. However, in such a safety-critical context, valid scene graphs can be further restricted by consistency constraints captured by domain or safety experts. However, existing ML approaches for scene graph generation focus exclusively on relational-level accuracy but provide little to no guarantee that consistency constraints are satisfied in the generated scene graphs. In this paper, we aim to complement existing ML-based approaches by a post-processing step using constraint optimization over probabilistic scene graphs that can (1) guarantee that no consistency constraints are violated and (2) improve the overall accuracy of the generated scene graphs by fixing constraint violations. We evaluate the effectiveness of our approach using well-known, and novel metrics in the context of two popular ML datasets augmented with consistency constraints and two ML-based scene graph generation approaches as baselines.