Deep learning-based low-light image enhancement (LLIE) is a task of leveraging deep neural networks to enhance the image illumination while keeping the image content unchanged. From the perspective of training data, existing methods complete the LLIE task driven by one of the following three data types: paired data, unpaired data and zero-reference data. Each type of these data-driven methods has its own advantages, e.g., zero-reference data-based methods have very low requirements on training data and can meet the human needs in many scenarios. In this paper, we leverage pure Gaussian noise to complete the LLIE task, which further reduces the requirements for training data in LLIE tasks and can be used as another alternative in practical use. Specifically, we propose Noise SElf-Regression (NoiSER) without access to any task-related data, simply learns a convolutional neural network equipped with an instance-normalization layer by taking a random noise image, N(0,σ2) for each pixel, as both input and output for each training pair, and then the low-light image is fed to the trained network for predicting the normal-light image. Technically, an intuitive explanation for its effectiveness is as follows: 1) the self-regression reconstructs the contrast between adjacent pixels of the input image, 2) the instance-normalization layer may naturally remediate the overall magnitude/lighting of the input image, and 3) the N(0,σ2) assumption for each pixel enforces the output image to follow the well-known gray-world hypothesis [1] when the image size is big enough. Compared to current state-of-the-art LLIE methods with access to different task-related data, NoiSER is highly competitive in enhancement quality, yet with a much smaller model size, and much lower training and inference cost. In addition, the experiments also demonstrate that NoiSER has great potential in overexposure suppression and joint processing with other restoration tasks.