Blind and universal image denoising consists of a unique model that denoises images with any level of noise. It is especially practical as noise levels do not need to be known when the model is developed or at test time. We propose a theoretically-grounded blind and universal deep learning image denoiser for Gaussian noise. Our network is based on an optimal denoising solution, which we call fusion denoising. It is derived theoretically with a Gaussian image prior assumption. Synthetic experiments show our network's generalization strength to unseen noise levels. We also adapt the fusion denoising network architecture for real image denoising. Our approach improves real-world grayscale image denoising PSNR results by up to 0.7dB for training noise levels and by up to 2.82dB on noise levels not seen during training. It also improves state-of-the-art color image denoising performance on every single noise level, by an average of 0.1dB, whether trained on or not.