Engineering design methods aim to generate new designs that meet desired performance requirements. Past work has directly introduced conditional Generative Adversarial Networks (cGANs) into this field and achieved promising results in single-point design problems(one performance requirement under one working condition). However, these methods assume that the performance requirements are distributed in categorical space, which is not reasonable in these scenarios. Although Continuous conditional GANs (CcGANs) introduce Vicinal Risk Minimization (VRM) to reduce the performance loss caused by this assumption, they still face the following challenges: 1) CcGANs can not handle multi-point design problems (multiple performance requirements under multiple working conditions). 2) Their training process is time-consuming due to the high computational complexity of the vicinal loss. To address these issues, A Continuous conditional Diffusion Probabilistic Model (CcDPM) is proposed, which the first time introduces the diffusion model into the engineering design area and VRM into the diffusion model. CcDPM adopts a novel sampling method called multi-point design sampling to deal with multi-point design problems. Moreover, the k-d tree is used in the training process of CcDPM to shorten the calculation time of vicinal loss and speed up the training process by 2-300 times in our experiments. Experiments on a synthetic problem and three real-world design problems demonstrate that CcDPM outperforms the state-of-the-art GAN models.