Neural data compression . Learned image compression methods are commonly based on hierarchical variational autoencoders [ 2,24,20 ] with a learned prior and latent variables being discretized for the purpose of entropy coding . In a similar vein to work in the latent variable model literature [ 14,19,16,22 ] , several works [ 5,12,38 ] attempt to close the amortization gap [ 8 ] by performing   iterative gradient - based optimization steps on top of the use of amortized inference networks . [ 38 ] additionally identify and attempt to close the discretization gap stemming from the quantization of the latent variables , also by inference time per - instance optimization . [ 37 ] take the idea of perinstance optimization of the model further : they perform per - instance finetuning of the decoder and transmit the quantized decoder parameter updates along with the latent code , leading to improved rate - distortion performance . In this paper , we take a different , and even more extreme from the per - instance optimization perspective , approach : we optimize an MLP to overfit a single image and transmit its weights as the compressed description of the image .