  The soft Dice loss (SDL) has taken a pivotal role in numerous automated
segmentation pipelines in the medical imaging community. Over the last years,
some reasons behind its superior functioning have been uncovered and further
optimizations have been explored. However, there is currently no implementation
that supports its direct utilization in scenarios involving soft labels. Hence,
a synergy between the use of SDL and research leveraging the use of soft
labels, also in the context of model calibration, is still missing. In this
work, we introduce Dice semimetric losses (DMLs), which (i) are by design
identical to SDL in a standard setting with hard labels, but (ii) can be
employed in settings with soft labels. Our experiments on the public QUBIQ,
LiTS and KiTS benchmarks confirm the potential synergy of DMLs with soft labels
(e.g. averaging, label smoothing, and knowledge distillation) over hard labels
(e.g. majority voting and random selection). As a result, we obtain superior
Dice scores and model calibration, which supports the wider adoption of DMLs in
practice. The code is available at https://github.com/zifuwanggg/JDTLosses
