Normalizing input for pre-trained model when unfreezing

From fastai lectures and the blogs that I am reading I know that one should normalize the data using pre-trained model’s statistics.

But what sould I do when:

  1. My data is different/very different from the data that the model is trained with (I think in this case using statistics of our data would be wiser)

  2. When I want to unfreeze the model, is it wise to use pre-trained model’s statistics ?

(for the question 2:
If I am not mistaken we should normalize our data using pre-trained model’s statistics because that model has learned via that statistics but I think if we unfreeze and that model using all of its layer, it would be wiser to normalize with our data.)

  1. If it is wiser to use our data’s statistics for normalizing when unfreezing, is it still the case when we unfreeze partially and then unfreeze completely?