  GFlowNets are a promising alternative to MCMC sampling for discrete
compositional random variables. Training GFlowNets requires repeated
evaluations of the unnormalized target distribution or reward function.
However, for large-scale posterior sampling, this may be prohibitive since it
incurs traversing the data several times. Moreover, if the data are distributed
across clients, employing standard GFlowNets leads to intensive client-server
communication. To alleviate both these issues, we propose embarrassingly
parallel GFlowNet (EP-GFlowNet). EP-GFlowNet is a provably correct
divide-and-conquer method to sample from product distributions of the form
$R(\cdot) \propto R_1(\cdot) ... R_N(\cdot)$ -- e.g., in parallel or federated
Bayes, where each $R_n$ is a local posterior defined on a data partition.
First, in parallel, we train a local GFlowNet targeting each $R_n$ and send the
resulting models to the server. Then, the server learns a global GFlowNet by
enforcing our newly proposed \emph{aggregating balance} condition, requiring a
single communication step. Importantly, EP-GFlowNets can also be applied to
multi-objective optimization and model reuse. Our experiments illustrate the
EP-GFlowNets's effectiveness on many tasks, including parallel Bayesian
phylogenetics, multi-objective multiset, sequence generation, and federated
Bayesian structure learning.
