Post date: Mar 13, 2017 7:10:1 PM
For a gentle tutorial on the topic, see [1]. My thoughts on this are:
Sum vs Max is the standard Forward vs Viterbi calculation.
Messages are generally assumed synchronous. Then the factor model between variable nodes results in the product of messages (over the same state).
Messages could be asynchronous, i.e. mutually exclusive.
[1] http://computerrobotvision.org/2009/tutorial_day/crv09_belief_propagation_v2.pdf