Deep learning (DL) training is data-intensive and often bottlenecked by fetching data from remote storage. Recognizing that many samples' sizes diminish during data preprocessing, we explore selectively offloading preprocessing to remote storage to mitigate data traffic. We conduct a case study to uncover the potential benefits and challenges of this approach. We then propose SOPHON, a framework that selectively offloads preprocessing tasks at a fine granularity in order to reduce data traffic, utilizing online profiling and adaptive algorithms to optimize for every sample in every training scenario. Our results show that SOPHON can reduce data traffic and training time by 1.2-2.2x over existing solutions.