Diffusion models represent a novel type of generative artificial intelligence models. Compared to traditional networks such as Generative Adversative Networks, Variational Autoencoders, and Flow models, diffusion models are characterized by their robust training, high fidelity and diversity in generation, and strong mathematical interpretability, and so they have been widely applied in fields of computer vision, signal processing, multi-modal learning and so on. Diffusion models are capable of sufficiently learning and exploring the deep generative priors from the training images, providing a novel paradigm for solving inverse problems in image processing. To systematically review the current developments of diffusion models, particularly the latest advancements in solving inverse problems in image processing, this paper provides a comprehensive survey on diffusion models for inverse problems in image processing. We firstly present its fundamental principles and recent developments, and then emphasize the introduction on the primary technical approaches as well as our specific application achievements for solving inverse problems in image processing. Finally, we outline the future research directions.