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Unsupervised domain adaptive hashing has emerged as a promising approach for efficient and memory-friendly cross-domain retrieval. It leverages the model learned on labeled source domains to generate compact binary codes for unlabeled target domain samples, ensuring that semantically similar samples are mapped to nearby points in the Hamming space. Existing methods typically apply domain adaptation techniques to the feature space or the Hamming space, especially pseudo-labeling and feature alignment. However, the inherent noise of pseudo-labels and the insufficient exploration of complementary knowledge across spaces hinder the ability of the adapted model. To address these challenges, we propose a Vision-language model assisted Pseudo-labeling and Dual Space adaptation (VPDS) method. Motivated by the strong zero-shot generalization capabilities of pre-trained vision-language models (VLMs), VPDS leverages VLMs to calibrate pseudo-labels, thereby mitigating pseudo-label bias. Furthermore, to simultaneously utilize the semantic richness of high-dimensional feature space and preserve discriminative efficiency of low-dimensional Hamming space, we introduce a dual space adaptation approach that performs independent alignment within each space. Extensive experiments on three benchmark datasets demonstrate that VPDS consistently outperforms existing methods in both cross-domain and single-domain retrieval tasks, highlighting its effectiveness and superiority.