Image denoising poses a significant challenge in image processing, aiming to remove noise and artifacts from input images. However, current denoising algorithms implemented on electronic chips frequently encounter latency issues and demand substantial computational resources. In this paper, we introduce an all-optical Nonlinear Diffractive Denoising Deep Network (N3DNet) for image denoising at the speed of light. Initially, we incorporate an image encoding and pre-denoising module into the Diffractive Deep Neural Network and integrate a nonlinear activation function, termed the phase exponential linear function, after each diffractive layer, thereby boosting the network's nonlinear modeling and denoising capabilities. Subsequently, we devise a new reinforcement learning algorithm called regularization-assisted deep Q-network to optimize N3DNet. Finally, leveraging 3D printing techniques, we fabricate N3DNet using the trained parameters and construct a physical experimental system for real-world applications. A new benchmark dataset, termed MIDD, is constructed for mode image denoising, comprising 120K pairs of noisy/noise-free images captured from real fiber communication systems across various transmission lengths. Through extensive simulation and real experiments, we validate that N3DNet outperforms both traditional and deep learning-based denoising approaches across various datasets. Remarkably, its processing speed is nearly 3,800 times faster than electronic chip-based methods.