Image denoising is an important problem in low-level vision and serves as a critical module for many image recovery tasks. Anisotropic diffusion is a wide family of image denoising approaches with promising performance. However, traditional anisotropic diffusion approaches use explicit diffusion operators which are not well adapted to complex image structures. As a result, their performance is limited compared to recent learning-based approaches. In this work, we describe a trainable anisotropic diffusion framework based on reinforcement learning. By modeling the denoising process as a series of naive diffusion actions with order learned by deep Q-learning, we propose an effective diffusion-based image denoiser. The diffusion actions selected by deep Q-learning at different iterations indeed composite a stochastic anisotropic diffusion process with strong adaptivity to different image structures, which enjoys improvement over the traditional ones. The proposed denoiser is applied to removing three types of often-seen noise. The experiments show that it outperforms existing diffusion-based methods and competes with the representative deep CNN-based methods.