Search papers, labs, and topics across Lattice.
This paper develops a unified theoretical framework for GFlowNet training, analyzing the relationship between balance objectives, approximate stationarity, and sampling accuracy. It provides novel bounds on terminal symmetric KL divergence in terms of expected balance loss and parameterization incompleteness, and establishes finite-time convergence guarantees under various backward policy update regimes. The work clarifies how parameterization, coverage, and moving components influence GFlowNet training dynamics and sampling fidelity.
GFlowNet sampling accuracy is fundamentally limited by the square root of balance loss and a parameterization incompleteness residual, with convergence rates established for diverse backward policy update strategies.
Generative Flow Networks (GFlowNets) learn policies that sample discrete objects in proportion to a positive reward. They are trained by minimizing balance objectives, whose exact satisfaction guarantees correct sampling. However, a comprehensive theory linking nonzero balance loss and approximate stationarity to sampling accuracy, especially under evolving sampling distributions and backward policies, is still lacking. To bridge this gap, we develop a unified theory for Flow Matching, Detailed Balance, and Trajectory Balance in this regime. We first bound terminal symmetric KL by the square root of the expected balance loss. Then, we show that approximate stationarity controls this distribution error up to a tangent-space residual measuring parameterization incompleteness. Finally, we establish finite-time convergence under fixed or controlled sampling and fixed, balance-trained, or separately updated backward policies. Under standard smoothness assumptions, with fixed or controlled sampling and a fixed or balance-trained backward policy, the expected loss is $O(\bar\epsilon^2+T^{-1})$ and expected terminal symmetric KL is $O(\bar\epsilon+T^{-1/2})$ under uniform coverage. For a separately updated backward policy, we characterize the sufficient update decay to approach the residual neighborhood and preserve these rates. These results connect balance objectives to sampling accuracy and clarify how parameterization, coverage, and moving components govern GFlowNet training.
