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Farmers frequently assess plant growth and performance as basis for making decisions when to take action in the field, such as fertilization, weed control, or harvesting. The prediction of plant growth is a major challenge, as it is affected by numerous and highly variable environmental factors. This paper proposes a novel monitoring approach that comprises high-throughput imaging sensor measurements and their automatic analysis to predict future plant growth. Our approach's core is a novel machine learning-based generative growth model based on conditional generative adversarial networks, which is able to predict the future appearance of individual plants. In experiments with RGB time-series images of laboratory-grown Arabidopsis thaliana and field-grown cauliflower plants, we show that our approach produces realistic, reliable, and reasonable images of future growth stages. The automatic interpretation of the generated images through neural network-based instance segmentation allows the derivation of various phenotypic traits that describe plant growth.