Current deep dehazing methods only focus on removing haze from hazy images, lacking the capability to translate between hazy and haze-free images. To address this issue, we propose a residual-based efficient bidirectional diffusion model (RBDM) that can model the conditional distributions for both dehazing and haze generation. Firstly, we devise dual Markov chains that can effectively shift the residuals and facilitate bidirectional smooth transitions between them. Secondly, the RBDM perturbs the hazy and haze-free images at individual timesteps and predicts the noise in the perturbed data to simultaneously learn the conditional distributions. Finally, to enhance performance on relatively small datasets and reduce computational costs, our method introduces a unified score function learned on image patches instead of entire images. Our RBDM successfully implements size-agnostic bidirectional transitions between haze-free and hazy images with only 15 sampling steps. Extensive experiments demonstrate that the proposed method achieves superior or at least comparable performance to state-of-the-art methods on both synthetic and real-world datasets.