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We investigate the task of learning blind image denoising networks from an unpaired set of clean and noisy images. Such problem setting generally is practical and valuable considering that it is feasible to collect unpaired noisy and clean images in most real-world applications. And we further assume that the noise can be signal dependent but is spatially uncorrelated. In order to facilitate unpaired learning of denoising network, this paper presents a two-stage scheme by incorporating self-supervised learning and knowledge distillation. For self-supervised learning, we suggest a dilated blind-spot network (D-BSN) to learn denoising solely from real noisy images. Due to the spatial independence of noise, we adopt a network by stacking 1x1 convolution layers to estimate the noise level map for each image. Both the D-BSN and image-specific noise model (CNN\_est) can be jointly trained via maximizing the constrained log-likelihood. Given the output of D-BSN and estimated noise level map, improved denoising performance can be further obtained based on the Bayes' rule. As for knowledge distillation, we first apply the learned noise models to clean images to synthesize a paired set of training images, and use the real noisy images and the corresponding denoising results in the first stage to form another paired set. Then, the ultimate denoising model can be distilled by training an existing denoising network using these two paired sets. Experiments show that our unpaired learning method performs favorably on both synthetic noisy images and real-world noisy photographs in terms of quantitative and qualitative evaluation.