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DNA points accumulation for imaging in nanoscale topography (DNA-PAINT) is a super-resolution technique with relatively easy-to-implement multi-target imaging. However, image acquisition is slow as sufficient statistical data has to be generated from spatio-temporally isolated single emitters. Here, we train the neural network (NN) DeepSTORM to predict fluorophore positions from high emitter density DNA-PAINT data. This achieves image acquisition in one minute. We demonstrate multi-colour super-resolution imaging of structure-conserved semi-thin neuronal tissue and imaging of large samples. This improvement can be integrated into any single-molecule imaging modality to enable fast single-molecule super-resolution microscopy.