Predicting Click-Through Rates is a crucial function within recommendation and advertising platforms, as the output of CTR prediction determines the order of items shown to users. The Embedding \& MLP paradigm has become a standard approach for industrial recommendation systems and has been widely deployed. However, this paradigm suffers from cold-start problems, where there is either no or only limited user action data available, leading to poorly learned ID embeddings. The cold-start problem hampers the performance of new items. To address this problem, we designed a novel diffusion model to generate a warmed-up embedding for new items. Specifically, we define a novel diffusion process between the ID embedding space and the side information space. In addition, we can derive a sub-sequence from the diffusion steps to expedite training, given that our diffusion model is non-Markovian. Our diffusion model is supervised by both the variational inference and binary cross-entropy objectives, enabling it to generate warmed-up embeddings for items in both the cold-start and warm-up phases. Additionally, we have conducted extensive experiments on three recommendation datasets. The results confirmed the effectiveness of our approach.