We develop a machine learning algorithm that generates high-resolution thermal Sunyaev-Zeldovich (SZ) maps of novel galaxy clusters given only halo mass and mass accretion rate. 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 the details of the aspherical turbulent galaxy clusters with a resolution similar to hydrodynamic simulations while achieving the computational feasibility of semi-analytical maps, allowing us to generate over $10^5$ mock SZ maps in 30 seconds on a laptop. We show that the individual images generated by the model are novel clusters (i.e. not found in the training set) and that the model accurately reproduces the effects of mass and mass accretion rate on the SZ images, such as scatter, asymmetry, and concentration, in addition to modeling merging sub-clusters. This work demonstrates the viability of machine-learning--based methods for producing the number of realistic, high-resolution maps of galaxy clusters necessary to achieve statistical constraints from future SZ surveys.