Multi-behavior recommender systems, which utilize auxiliary behaviors (e.g., page view, add-to-favorite, and add-to-cart) to assist in predicting user target behaviors (e.g., purchase), are regarded as an effective way to enhance recommendation accuracy and improve user experience. However, noisy and irrelevant information often exists in auxiliary behaviors, which can mislead target behavior predictions and worsen the semantic gap between target and auxiliary behaviors. To address the above challenges, we propose a denoising Diffusion Multi-Behavior Recommender model (DMBR). First, our method employs a graph diffusion paradigm to mitigate the noisy effects in the auxiliary behavior interaction graph. Specifically, we introduce a customized denoising module and a semantic injection mechanism, both leveraging collaborative relationship semantics from target behaviors to guide our graph diffusion process. Then, we predict user target behaviors by leveraging a dual graph learning encoder to model both the target behavior graph and the denoised auxiliary behavior graph. Moreover, our graph learning encoder is equipped with a semantic transfer unit to bridge the semantic gap between behaviors. Experimental results demonstrate the superiority of our DMBR over various state-of-the-art baselines.