Cross-domain sequential recommendation aims to alleviate data sparsity and cold-start problems by transferring useful preference knowledge across domains. However, users exhibit varying degrees of preference consistency across domains, while existing methods often rely on global alignment objectives or coarse-grained transfer strategies. Such approaches may introduce irrelevant information and provide limited flexibility in adapting semantic representations to individual user preferences. To address these challenges, we propose BGAFlow, a personalized framework that combines state-adaptive semantic evolution with user-specific transfer control. BGAFlow first establishes a shared semantic space through unified dual-domain pretraining with user profiles inferred by a large language model (LLM). Based on latent interest overlap, it then estimates a personalized horizon to determine the appropriate transfer extent for each user. To enable semantic adaptation, BGAFlow constructs a conditional Bezier curve as a geometric reference and learns a residual flow that progressively refines the trajectory based on intermediate preference states. The learned flow incorporates dynamic preference feedback to adjust transfer directions, while recommendation supervision and trajectory regularization encourage effective and smooth adaptation. Extensive experiments on real-world datasets demonstrate that BGAFlow consistently outperforms state-of-the-art baselines, validating the benefits of personalized transfer control and state-adaptive semantic evolution.

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