Question on confidence in training metric model

The metric depth model does not predict confidence noted [here](https://github.com/ByteDance-Seed/Depth-Anything-3/issues/103). In the paper, it is noted metric depth is trained using $L_{depth}$ $L_{grad}$ and $L_{sky}$ (4.4 Implementation Details). But $L_{depth}$ uses a confidence map (3.3 Training Objectives).

What is the confidence map used for teaching metric depth if it does not produce one itself?

If it uses some confidence map, how does one prevent high confidence map values from creating a negative loss with the second term in $L_{depth}$? I'm guessing $D_c$ is bounded somehow but the code does not seem to suggest that.

What is $\lambda_c$ value?

Thanks for cool work!