Key Information Extraction (KIE) converts visually rich documents into structured data, but practical deployment remains challenging: strong performance often relies on costly on-server Large Multimodal Models (LMMs), while compact locally deployable models lack sufficient KIE supervision. We present SAYRE, a scene-aware document synthesis framework for generating scalable KIE training data without hand-crafted template design. Given a few exemplar documents, SAYRE captures category-specific content patterns and layout conventions to synthesize document-schema-annotation triples. It further introduces error-driven generation, which expands real-world failure cases into hard training examples while preserving their structural patterns. Experiments on constrained- and open-category KIE show that SAYRE consistently improves Qwen3-VL backbones and achieves the strongest overall performance among on-device LMMs. Data scaling experiments show an overall upward trend as more synthesized data is introduced, especially for smaller models and open-category extraction. Error analysis further shows that synthesized training reduces field-level errors by improving schema-aware extraction over dense tables, business identifiers, and contract clauses. These results establish scene-aware synthesis as an effective data-centric approach for improving practical multimodal KIE.

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