I am not into the field of super resolution but I think this question applies to general neural network construction.

Usually you try to solve a classification problem or a regression problem with your neural network.

 - For classification you try to predict probabilities that a specific
   output corrensponds to a specific class. Therefore every output value
   should be a probability and therefore have a range between 0 and 1.
   To achieve this you usually use a softmax or sigmoid function as your
   last layer to squash the output between 0 and 1 and give likely
   classes higher probabilities and unlikely classes less probability.

 - For the regression task you are not looking for probability values as
   your output values but instead for real numbers. In such a case no
   activation function is wanted since you want to be able to
   approximate any possible real value and not probabilities.

So in the case of super resolution I think the generated output is a map where each value corresponds to a pixel value of the super resolution image. In that case your pixels are real number values and no probabilities. So you are solving a regression problem.