Generative summarization is a critical task in natural language processing, aiming to generate concise and accurate information from large volumes of text. The current mainstream generative summarization model employs a deep learning-based sequence-to-sequence architecture, with optimization performed at the character level. However, due to insufficient attention to semantic consistency between generated summaries and the source text, these models often produce outputs with semantic ambiguity and factual inaccuracies. To tackle this challenge, we propose OpenFactAlign, a novel framework that enhances factual consistency by dynamically extracting and aligning open-domain facts with summaries. The framework extracts open-domain triples (subject-predicate-object structures) as factual knowledge from raw text and introduces a loss function to minimize semantic deviation. By enhancing the semantic representation of factual knowledge during decoding, the model generates summaries with improved alignment to the source text. Extensive experiments on the LCSTS dataset demonstrate that the proposed model achieves improvements of 6.06, 6.88 and 3.09% points in ROUGE-1, ROUGE-2 and ROUGE-L scores, respectively, and 5.7, 8.31, 0.86 and 2.11% points in BLEU-1, BLEU-2, BLEU-3 and BLEU-4 scores, respectively, compared to the BART baseline.