  We propose a method to infer a dense depth map from a single image, its
calibration, and the associated sparse point cloud. In order to leverage
existing models (teachers) that produce putative depth maps, we propose an
adaptive knowledge distillation approach that yields a positive congruent
training process, wherein a student model avoids learning the error modes of
the teachers. In the absence of ground truth for model selection and training,
our method, termed Monitored Distillation, allows a student to exploit a blind
ensemble of teachers by selectively learning from predictions that best
minimize the reconstruction error for a given image. Monitored Distillation
yields a distilled depth map and a confidence map, or ``monitor'', for how well
a prediction from a particular teacher fits the observed image. The monitor
adaptively weights the distilled depth where if all of the teachers exhibit
high residuals, the standard unsupervised image reconstruction loss takes over
as the supervisory signal. On indoor scenes (VOID), we outperform blind
ensembling baselines by 17.53% and unsupervised methods by 24.25%; we boast a
79% model size reduction while maintaining comparable performance to the best
supervised method. For outdoors (KITTI), we tie for 5th overall on the
benchmark despite not using ground truth. Code available at:
https://github.com/alexklwong/mondi-python.
