Model for image regression

I would like to train model to label every pixel in an image with a continuous value, as opposed to discrete categories in typical semantic segmentation.
Is this as simple as altering the error metric and removing the argmax at the end something like Segformer? Or are there more specialized networks for this type of problem?

I have struggled to find examples of this exact case to examine, the closest being perhaps monocular depth estimation, but I’m not sure how biased a fine tuning on those would be.

Thanks in advance!