Many deep learning-based solutions to blind image deblurring estimate the blur representation and reconstruct the target image from its blurry observation. However, these methods suffer from severe performance degradation in real-world scenarios because they ignore important prior information about motion blur (e.g., real-world motion blur is diverse and spatially varying). Some methods have attempted to explicitly estimate non-uniform blur kernels by CNNs, but accurate estimation is still challenging due to the lack of ground truth about spatially varying blur kernels in real-world images. To address these issues, we propose to represent the field of motion blur kernels in a latent space by normalizing flows, and design CNNs to predict the latent codes instead of motion kernels. To further improve the accuracy and robustness of non-uniform kernel estimation, we introduce uncertainty learning into the process of estimating latent codes and propose a multi-scale kernel attention module to better integrate image features with estimated kernels. Extensive experimental results, especially on real-world blur datasets, demonstrate that our method achieves state-of-the-art results in terms of both subjective and objective quality as well as excellent generalization performance for non-uniform image deblurring. The code is available at https://see.xidian.edu.cn/faculty/wsdong/Projects/UFPNet.htm.