ABSTRACT We develop a machine-learning (ML) algorithm that generates high-resolution thermal Sunyaev–Zeldovich (SZ) maps of novel galaxy clusters given only halo mass and mass accretion rate (MAR). The algorithm uses a conditional variational autoencoder (CVAE) in the form of a convolutional neural network and is trained with SZ maps generated from the IllustrisTNG simulation. Our method can reproduce many of the details of galaxy clusters that analytical models usually lack, such as internal structure and aspherical distribution of gas created by mergers, while achieving the same computational feasibility, allowing us to generate mock SZ maps for over 105 clusters in 30 s on a laptop. We show that the model is capable of generating novel clusters (i.e. not found in the training set) and that the model accurately reproduces the effects of mass and MAR on the SZ images, such as scatter, asymmetry, and concentration, in addition to modelling merging sub-clusters. This work demonstrates the viability of ML-based methods for producing the number of realistic, high-resolution maps of galaxy clusters necessary to achieve statistical constraints from future SZ surveys.