Prevalent lossy image compression schemes can be divided into: 1) explicit image compression (EIC), including traditional standards and neural end-to-end algorithms; 2) implicit image compression (IIC) based on implicit neural representations (INR). The former is encountering impasses of either leveling off bitrate reduction at a cost of tremendous complexity while the latter suffers from excessive smoothing quality as well as lengthy decoder models. In this paper, we propose an innovative paradigm, which we dub \textbf{Unicorn} (\textbf{U}nified \textbf{N}eural \textbf{I}mage \textbf{C}ompression with \textbf{O}ne \textbf{N}number \textbf{R}econstruction). By conceptualizing the images as index-image pairs and learning the inherent distribution of pairs in a subtle neural network model, Unicorn can reconstruct a visually pleasing image from a randomly generated noise with only one index number. The neural model serves as the unified decoder of images while the noises and indexes corresponds to explicit representations. As a proof of concept, we propose an effective and efficient prototype of Unicorn based on latent diffusion models with tailored model designs. Quantitive and qualitative experimental results demonstrate that our prototype achieves significant bitrates reduction compared with EIC and IIC algorithms. More impressively, benefitting from the unified decoder, our compression ratio escalates as the quantity of images increases. We envision that more advanced model designs will endow Unicorn with greater potential in image compression. We will release our codes in \url{https://github.com/uniqzheng/Unicorn-Laduree}.
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