What the network actually predicts

A single image is consistent with infinitely many scenes. Double every distance and double the size of every object and the image is pixel-identical. No amount of architecture removes that: the mapping from image to metric depth is not a function, and a network that appears to compute it is doing something else.

What it is doing is exploiting a prior. Doors are about two metres tall, roads are about as wide as two cars, texture gradients fall off in a characteristic way, and objects that occlude are in front. These are statistical regularities of the training distribution, and they are enormously informative — which is why monocular depth works at all — and they are not geometry, which is why it fails in specific and predictable ways.

The reason relative models predict in disparity space is worth spelling out. In depth space, a metre of error at $2$ m and a metre at $50$ m are the same loss, so a network trained with an $L_1$ depth loss spends its capacity on the far field, where the geometry is least informative and the labels are worst. In disparity space, $1/Z$ compresses the far field: the same loss now weights the near field, where the pixels are dense and the labels are good.

That is a defensible modelling choice with a real consequence — the model is accurate where disparity is large and vague where it is small — and it is why comparing two models that predict in different spaces requires care.