Vision-Language Models (VLMs) generate discourse-level, multi-sentence visual descriptions, challenging text scene graph parsers built for single-sentence caption-to-graph mapping.Current approaches typically merge sentencelevel parsing outputs for discourse input, often missing phenomena like cross-sentence coreference, resulting in fragmented graphs and degraded downstream VLM task performance.We introduce a new task, Discourse-level text Scene Graph parsing (DiscoSG), and release DiscoSG-DS, a dataset of 400 expert-annotated and 8,430 synthesised multi-sentence captiongraph pairs.Each caption averages 9 sentences, and each graph contains at least 3× more triples than those in existing datasets.Fine-tuning GPT-4o on DiscoSG-DS yields over 40% higher SPICE metric than the best sentence-merging baseline.However, its high inference cost and licensing restrict opensource use.Smaller fine-tuned open-source models (e.g., Flan-T5) perform well on simpler graphs yet degrade on denser, more complex graphs.To bridge this gap, we introduce DiscoSG-Refiner, a lightweight open-source parser that drafts a seed graph and iteratively refines it with a novel learned graph-editing model, achieving 30% higher SPICE than the baseline while delivering 86× faster inference than GPT-4o.It generalises from simple to dense graphs, thereby consistently improving downstream VLM tasks, including discourselevel caption evaluation and hallucination detection, outperforming alternative open-source parsers.