Our hypothesis is that UDA using diffusion-weighted images, generated with a unified model, offers a promising and reliable strategy for enhancing the performance of supervised learning models in multi-site prostate lesion detection, especially when various b-values are present. This retrospective study included data from 5,150 patients (14,191 samples) collected across nine different imaging centers. A novel UDA method using a unified generative model was developed for multi-site PCa detection. This method translates diffusion-weighted imaging (DWI) acquisitions, including apparent diffusion coefficient (ADC) and individual DW images acquired using various b-values, to align with the style of images acquired using b-values recommended by Prostate Imaging Reporting and Data System (PI-RADS) guidelines. The generated ADC and DW images replace the original images for PCa detection. An independent set of 1,692 test cases (2,393 samples) was used for evaluation. The area under the receiver operating characteristic curve (AUC) was used as the primary metric, and statistical analysis was performed via bootstrapping. For all test cases, the AUC values for baseline SL and UDA methods were 0.73 and 0.79 (p<.001), respectively, for PI-RADS>=3, and 0.77 and 0.80 (p<.001) for PI-RADS>=4 PCa lesions. In the 361 test cases under the most unfavorable image acquisition setting, the AUC values for baseline SL and UDA were 0.49 and 0.76 (p<.001) for PI-RADS>=3, and 0.50 and 0.77 (p<.001) for PI-RADS>=4 PCa lesions. The results indicate the proposed UDA with generated images improved the performance of SL methods in multi-site PCa lesion detection across datasets with various b values, especially for images acquired with significant deviations from the PI-RADS recommended DWI protocol (e.g. with an extremely high b-value).