Why add noise and how to calculate the logdet of this operation

[Le2Hu]

https://github.com/andreas128/SRFlow/blob/5a007ad591c7be8bf32cf23171bfa4473e71683c/code/models/modules/SRFlowNet_arch.py#L92-L97

According to the lines, uniform noise between [-0.5,0.5) is added into the input image, is the operation necessary? And why the logdet should be updated like this? When I read the paper, I noticed the description in the trainning details section as below, but i am not sure whether it's implemented by the mentioned lines or not.

adding slight random noise to the target image helps the training process and leads to better visual results. We therefore add Gaussian noise with a standard deviation of $\sigma = 4/ \sqrt 3$ to the high-resolution image. In contrast to [21], we do not employ 5-bit quantization.