Overfitting to synthetic training pairs remains a critical challenge in image dehazing, leading to poor generalization capability to real-world scenarios. To address this issue, existing approaches utilize unpaired realistic data for training, employing CycleGAN or contrastive learning frameworks. Despite their progress, these methods often suffer from training instability, resulting in limited dehazing performance. In this paper, we propose a novel training strategy for unpaired image dehazing, termed Rehazy, to improve both dehazing performance and training stability. This strategy explores the consistency of the underlying clean images across hazy images and utilizes hazy-rehazy pairs for effective learning of real haze characteristics. To favorably construct hazy-rehazy pairs, we develop a physics-based rehazy generation pipeline, which is theoretically validated to reliably produce high-quality rehazy images. Additionally, leveraging the rehazy strategy, we introduce a dual-branch framework for dehazing network training, where a clean branch provides a basic dehazing capability in a synthetic manner, and a hazy branch enhances the generalization ability with hazy-rehazy pairs. Moreover, we design a new dehazing network within these branches to improve the efficiency, which progressively restores clean scenes from coarse to fine. Extensive experiments on four benchmarks demonstrate the superior performance of our approach, exceeding the previous state-of-the-art methods by 3.58 dB on the SOTS-Indoor dataset and by 1.85 dB on the SOTS-Outdoor dataset in PSNR. Our code will be publicly available.