The successful deployment of artificial intelligence (AI) in many domains from healthcare to hiring requires their responsible use, particularly in model explanations and privacy. Explainable artificial intelligence (XAI) provides more information to help users to understand model decisions, yet this additional knowledge exposes additional risks for privacy attacks. Hence, providing explanation harms privacy. We study this risk for image-based model inversion attacks and identified several attack architectures with increasing performance to reconstruct private image data from model explanations. We have developed several multi-modal transposed CNN architectures that achieve significantly higher inversion performance than using the target model prediction only. These XAI-aware inversion models were designed to exploit the spatial knowledge in image explanations. To understand which explanations have higher privacy risk, we analyzed how various explanation types and factors influence inversion performance. In spite of some models not providing explanations, we further demonstrate increased inversion performance even for non-explainable target models by exploiting explanations of surrogate models through attention transfer. This method first inverts an explanation from the target prediction, then reconstructs the target image. These threats highlight the urgent and significant privacy risks of explanations and calls attention for new privacy preservation techniques that balance the dual-requirement for AI explainability and privacy.