  Generative Flow Networks (GFlowNets) have been introduced as a method to
sample a diverse set of candidates in an active learning context, with a
training objective that makes them approximately sample in proportion to a
given reward function. In this paper, we show a number of additional
theoretical properties of GFlowNets. They can be used to estimate joint
probability distributions and the corresponding marginal distributions where
some variables are unspecified and, of particular interest, can represent
distributions over composite objects like sets and graphs. GFlowNets amortize
the work typically done by computationally expensive MCMC methods in a single
but trained generative pass. They could also be used to estimate partition
functions and free energies, conditional probabilities of supersets
(supergraphs) given a subset (subgraph), as well as marginal distributions over
all supersets (supergraphs) of a given set (graph). We introduce variations
enabling the estimation of entropy and mutual information, sampling from a
Pareto frontier, connections to reward-maximizing policies, and extensions to
stochastic environments, continuous actions and modular energy functions.
