Abstract: Explicit deep generative models (DGMs), e.g., VAEs and Normalizing Flows, have shown to offer an effective data modelling alternative for lossless compression. However, DGMs themselves normally require large storage space and thus contaminate the advantage brought by accurate data density estimation.To eliminate the requirement of saving separate models for different target datasets, we propose a novel setting that starts from a pretrained deep generative model and compresses the data batches while adapting the model with a dynamical system for only one epoch.We formalise this setting as that of One-Shot Online Adaptation (OSOA) of DGMs for lossless compression and propose a vanilla algorithm under this setting. Experimental results show that vanilla OSOA can save significant time versus training bespoke models and space versus using one model for all targets.With the same adaptation step number or adaptation time, it is shown vanilla OSOA can exhibit better space efficiency, e.g., $47\%$ less space, than fine-tuning the pretrained model and saving the fine-tuned model.Moreover, we showcase the potential of OSOA and motivate more sophisticated OSOA algorithms by showing further space or time efficiency with multiple updates per batch and early stopping.