In recent years, the number of digital images has grown exponentially because of the widespread use of fast internet and smart devices. The integrity authentication of these images is a major concern for the research community. So, the encryption schemes that are commonly used to protect these images are an important subject for many potential applications. This paper presents a comprehensive survey of recent image encryption techniques using deep learning models. First, we explain the reasons that image encryption using deep learning models is beneficial to researchers and the public. Second, we discuss various state-of-art encryption techniques using deep learning models and offer technical summaries of popular techniques. Third, we provide a comparative analysis of our survey and existing state-of-the-art surveys. Finally, by investigating existing deep learning-based encryption, we identify several important research challenges and possible solutions including standard security metrics. To the best of our knowledge, we are the first researchers to do a detailed survey of deep learning-based image encryption for digital images.