Most current MKGC approaches are predominantly based on discriminative models that maximize conditional likelihood. These approaches struggle to efficiently capture the complex connections in real-world knowledge graphs, thereby limiting their overall performance. To address this issue, we propose a structure-aware multimodal Diffusion model for multimodal knowledge graph Completion (DiffusionCom). DiffusionCom innovatively approaches the problem from the perspective of generative models, modeling the association between the $(head, relation)$ pair and candidate tail entities as their joint probability distribution $p((head, relation), (tail))$, and framing the MKGC task as a process of gradually generating the joint probability distribution from noise. Furthermore, to fully leverage the structural information in MKGs, we propose Structure-MKGformer, an adaptive and structure-aware multimodal knowledge representation learning method, as the encoder for DiffusionCom. Structure-MKGformer captures rich structural information through a multimodal graph attention network (MGAT) and adaptively fuses it with entity representations, thereby enhancing the structural awareness of these representations. This design effectively addresses the limitations of existing MKGC methods, particularly those based on multimodal pre-trained models, in utilizing structural information. DiffusionCom is trained using both generative and discriminative losses for the generator, while the feature extractor is optimized exclusively with discriminative loss. This dual approach allows DiffusionCom to harness the strengths of both generative and discriminative models. Extensive experiments on the FB15k-237-IMG and WN18-IMG datasets demonstrate that DiffusionCom outperforms state-of-the-art models.