Particle GFlowNets: Rethinking Generative Marginalization Models

This paper explores policy gradient algorithms for training stochastic policies to sample from structured discrete probability distributions under the Generative Flow Network (GFlowNet) framework. Building on extensive theoretical connections between GFlowNets and entropy-regularized reinforcement learning, we derive equivalents of standard policy gradient algorithms for training GFlowNets, as well as experimentally explore their various methodological aspects, including baseline training and advantage estimation. Most importantly, our work is the first to derive and successfully apply proximal policy optimization to GFlowNets, showing its improved convergence speed and data efficiency compared to standard GFlowNet training objectives on benchmarks ranging from synthetic energies to molecular graph generation.

Mean-field games (MFGs) offer a unifying lens on continuous-time generative modeling: a cost tuple recovering twelve prominent models---Continuous Normalizing Flows, OT-Flow, Score-based Models, Schrödinger Bridges, and more---as special cases of one variational problem. Yet two dimensions of this space remain entirely unexplored: the interaction term $\mathcal{I}$ is set to zero in many existing models, and the rich family of MFG solvers has never been applied to generative modeling. We address both gaps with MFGLab an open-source PyTorch library whose primary API is the cost tuple: all twelve models are specified by four composable cost functions, and the training loop, log-Jacobian, and reverse-ODE sampler are shared automatically. We additionally propose DI-Flow, a novel cost design that uses a differentiable entropy functional to encourage mode coverage, and provide learning-based MFG solvers that substantially outperform neural training on stochastic-dynamics rows. Experiments on two 2-D benchmarks confirm that the unified API is lossless relative to hand-coded implementations.

We present GFlowState, a visual analytics system designed to illuminate the training process of Generative Flow Networks (GFlowNets or GFNs). GFlowNets are a probabilistic framework for generating samples proportionally to a reward function. While GFlowNets have proved to be powerful tools in applications such as molecule and material discovery, their training dynamics remain difficult to interpret. Standard machine learning tools allow metric tracking but do not reveal how models explore the sample space, construct sample trajectories, or shift sampling probabilities during training. Our solution, GFlowState, allows users to analyze sampling trajectories, compare the sample space relative to reference datasets, and analyze the training dynamics. To this end, we introduce multiple views, including a chart of candidate rankings, a state projection, a node-link diagram of the trajectory network, and a transition heatmap. These visualizations enable GFlowNet developers and users to investigate sampling behavior and policy evolution, and to identify underexplored regions and sources of training failure. Case studies demonstrate how the system supports debugging and assessing the quality of GFlowNets across application domains. By making the structural dynamics of GFlowNets observable, our work enhances their interpretability and can accelerate GFlowNet development in practice.