A consistency checker is configured to perform repairs to one or more multi-level dense tree metadata structures shared between volumes managed by a volume layer of a storage input/output (I/O) stack executing on one or more nodes of a cluster. The volumes include a parent volume and a snapshot and/or clone, wherein the snapshot/clone may be represented as an independent volume, and embodied as a respective read-only copy (snapshot) or read-write copy (clone) of the parent volume. Illustratively, the consistency checker verifies and/or fixes (i.e., repairs) on-disk structures of the volume layer, e.g., the shared dense tree, according to a distributed repair procedure that maintains consistency properties across all volumes in a volume family and avoid cyclic repairs made in the context of different volumes sharing the dense tree.