We study the generalization properties of deep convolutional neural networks for image denoising in the presence of varying noise levels. We provide extensive empirical evidence that current state-of-the-art architectures systematically overfit to the noise levels in the training set, performing very poorly at new noise levels. We show that strong generalization can be achieved through a simple architectural modification: removing all additive constants. The resulting "bias-free" networks attain state-of-the-art performance over a broad range of noise levels, even when trained over a narrow range. They are also locally linear, which enables direct analysis with linear-algebraic tools. We show that the denoising map can be visualized locally as a filter that adapts to both image structure and noise level. In addition, our analysis reveals that deep networks implicitly perform a projection onto an adaptively-selected low-dimensional subspace, with dimensionality inversely proportional to noise level, that captures features of natural images.
This paper looks at how deep convolutional neural networks for image denoising can generalize across various noise levels. First, they argue that state-of-the-art denoising networks perform poorly outside of the training noise range. The authors empirically show that as denoising performance degrades on unseen noise levels, the network residual for a specific input is being increasingly dominated by the network bias (as opposed to the purely linear Jacobian term). Therefore, they propose using bias-free convolutional neural networks for better generalization performance in image denoising. Their experimental results show that bias-free denoisers significantly outperform their original counter-parts on unseen noise levels across various popular architectures. Then, they perform a local analysis of the bias-free network around an input image that is now a strictly linear function of the input. They empirically demonstrate that the Jacobian is approximately low-rank and symmetric, therefore the effect of the denoiser can be interpreted as a nonlinear adaptive filter that projects the noisy image onto a low-dimensional signal subspace. The authors show that most of the energy of the clean image falls into the signal subspace and the effective dimensionality of this subspace is inversely proportional to the noise level.
Even though it is theoretically not too well-motivated in the paper why the bias term degrades generalization performance, the experimental results seem to clearly demonstrate the merit of bias-free denoisers. Moreover, the analysis of the network Jacobian and its interpretation as a nonlinear adaptive filter provides some interesting insight in the local properties of bias-free denoisers. Therefore, I would recommend accepting this paper, if the authors provide a theoretical discussion on why the bias term might degrade generalization performance.
Some smaller comments: 
-It is not clear if d should be multiplied by \sigma^2 in its definition on page 7. The definition mentions dependence on noise variance, but the formula does not have it.
-In Section 3 in the expression of the mean squared error it is not defined what g(y) means.
-Axis labels are missing on Fig. 3.