This study uses a sigma-variational autoencoder to learn a latent space of the Sun using the 12 channels taken by Atmospheric Imaging Assembly (AIA) and the Helioseismic and Magnetic Imager (HMI) instruments on-board the NASA Solar Dynamics Observatory. The model is able to significantly compress the large image dataset to 0.19% of its original size while still proficiently reconstructing the original images. As a downstream task making use of the learned representation, this study demonstrates the of use the solar latent space as an input to improve the forecasts of the F30 solar radio flux index, compared to an off-the-shelf pretrained ResNet feature extractor. Finally, the developed models can be used to generate realistic synthetic solar images by sampling from the learned latent space.