Although deep neural network (DNN)-based speech enhancement (SE) methods outperform the previous non-DNN-based ones, they often degrade the perceptual quality of generated outputs. To tackle this problem, we introduce a DNN-based generative refiner, Diffiner, aiming to improve perceptual speech quality pre-processed by an SE method. We train a diffusion-based generative model by utilizing a dataset consisting of clean speech only. Then, our refiner effectively mixes clean parts newly generated via denoising diffusion restoration into the degraded and distorted parts caused by a preceding SE method, resulting in refined speech. Once our refiner is trained on a set of clean speech, it can be applied to various SE methods without additional training specialized for each SE module. Therefore, our refiner can be a versatile post-processing module w.r.t. SE methods and has high potential in terms of modularity. Experimental results show that our method improved perceptual speech quality regardless of the preceding SE methods used.