Cave Corals are very small speleothems consisting of short stalks with bulbous ends. As a result of their characteristic forms they are also dubbed Cave Popcorn or Coralloids, sometimes they are called bulbuous calcite, which is actually a wider term and includes other forms of speleothems. They usually occur in groups and cover wall and ceiling surfaces. They have a slightly thinner base or stem and a mostly rounded head. Inside, they are built up in layers, you can clearly see at the fracture surfaces of the damaged cave corals in the pictures. The sinter is therefore similar to the sinter of stalactites, which suggests that they are deposited from a thin film of water. They grow in all directions and ignore gravity. The formation mechanisms for this type of sinter are largely unknown. There are a number of theories, none of which are really convincing, and they are generally only attempts to explain one aspect.
To summarise, cave coral is by far the most mysterious cave mineral. There is no conclusive and reasonably detailed explanation of how they are formed. However, this is probably also due to the fact that there has been no serious scientific work on this speleothem to date. Anyone looking for a topic for a doctoral thesis has an interesting task here.