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We present a model for generating postage stamp images of synthetic Fanaroff-Riley Class I and Class II radio galaxies suitable for use in simulations of future radio surveys such as those being developed for the Square Kilometre Array. This model uses a fully-connected neural network to implement structured variational inference through a variational auto-encoder and decoder architecture. In order to optimise the dimensionality of the latent space for the auto-encoder we introduce the radio morphology inception score (RAMIS), a quantitative method for assessing the quality of generated images, and discuss in detail how data pre-processing choices can affect the value of this measure. We examine the 2-dimensional latent space of the VAEs and discuss how this can be used to control the generation of synthetic populations, whilst also cautioning how it may lead to biases when used for data augmentation.