Combining a diffusion model with a sparse coding strategy to improve the machine translation accuracy of culturally loaded words in English news texts

News texts are characterized by their timeliness, contextual dependence, and density of proper nouns. Cultural terms, often appearing as metaphors, allusions, or institutional terms, are frequently long-tailed words lacking sufficient corpus support, easily leading to semantic drift and cultural information loss in translation. To address these issues, this paper combines a diffusion model with a sparse coding strategy to improve the accuracy and cultural adaptability of cultural terms in English news translation. In the encoding stage, a sparse semantic extraction module based on L1 norm constraints and dictionary learning is constructed to sparsely represent the input sequence, strengthening the expression of key information about cultural terms. In the decoding stage, a diffusion generation mechanism is introduced to gradually reconstruct the target text through multi-step denoising. Simultaneously, by combining time-step-aware gating and cultural ontology knowledge constraints, end-to-end collaborative optimization of cultural feature extraction and target language generation is achieved. Experimental results show that compared with mainstream models such as Transformer, mBART-50 (many to many multilingual machine translation), and DiffuSeq (Sequence to sequence text generation with diffusion models), proposed model achieves BLEU (Bilingual Evaluation Understudy)-4 and METEOR (Metric for Evaluation of Translation with Explicit Ordering) scores of 27.8% and 29.2%, respectively, on long-tail news text (sentences of 46 words or more). In the unregistered vocabulary scenario, the accuracy and recall rates were 73.7% and 65.2%, respectively, and the cultural semantic consistency index reached 0.892. The results indicate that the proposed synergistic mechanism of sparse coding and diffusion generation facilitates weak semantic recognition and progressive semantic restoration, providing a technical path for cross-cultural machine translation in international news communication that combines accuracy with cultural adaptability.