This work proposes a learning-based statistical refinement method for improving the denoising results of a given denoiser without knowing the precise noise distribution or accessing clean images or calibration data. While there are many existing successful denoising approaches for handling different kinds of noise, they typically require accurate modelling of the images and the noise (implicitly or explicitly), and hence the denoising results can be suboptimal due to different practical factors such as imperfect models, unreliable noise assumptions, or low quality data. In particular, when clean image samples are not available and there is a lack of knowledge of the underlying noise distribution, which is the case in various practical situations, the results may not well align with the noise statistics. The unawareness of the useful statistical information leads to suboptimal results. This work aims to make the best use of the statistical information to improve the consistency between the given denoising results and the noise statistics, under the assumption that the noise is conditionally pixel-wise independent given the clean signal. A method, based on a Bayesian formulation of an auxiliary signal in the noisy data, is proposed for evaluating the consistency of the denoising results, without precise information on noise distribution. By leveraging the statistical information from noisy data, the method enhances the statistical noise consistency and improves denoising quality.