Abstract: Neural data compression has been shown to outperform classical methods in terms of $RD$ performance, with results still improving rapidly. At a high level, neural compression is based on an autoencoder that tries to reconstruct the input instance from a (quantized) latent representation, coupled with a prior that is used to losslessly compress these latents. Due to limitations on model capacity and imperfect optimization and generalization, such models will suboptimally compress test data in general. However, one of the great strengths of learned compression is that if the test-time data distribution is known and relatively low-entropy (e.g. a camera watching a static scene, a dash cam in an autonomous car, etc.), the model can easily be finetuned or adapted to this distribution, leading to improved $RD$ performance. In this paper we take this concept to the extreme, adapting the full model to a single video, and sending model updates (quantized and compressed using a parameter-space prior) along with the latent representation. Unlike previous work, we finetune not only the encoder/latents but the entire model, and - during finetuning - take into account both the effect of model quantization and the additional costs incurred by sending the model updates. We evaluate an image compression model on I-frames (sampled at 2 fps) from videos of the Xiph dataset, and demonstrate that full-model adaptation improves $RD$ performance by ~1 dB, with respect to encoder-only finetuning.