Learning a Mixture of GFlowNets

2026-10-05

AI Summary

This study addresses the high computational overhead and lack of theoretical grounding in GFlowNet ensemble sampling by establishing a general theoretical framework for hybrid GFlowNets, introducing the first unified formulation of continuous and discrete indexing. Methodologically, it incorporates a hierarchical conditioning mechanism inspired by the Doob h-transform to decompose the state space, and optimizes sampling efficiency through random feature expansion, spectral shift analysis, and a parallel training architecture. This work significantly improves learning convergence speed and mode coverage without introducing additional computational costs, thereby providing both a theoretical and algorithmic foundation for efficient generative flow networks.

Abstract

Learning an ensemble of GFlowNets to sample from a discrete target distribution has become a common approach for achieving better state space exploration and convergence than that of a monolithic sampler. However, these methods often add a substantial runtime overhead to the base model, and their conceptual connection remains elusive. To address this, we first propose a general-purpose theoretical framework for describing a mixture of GFlowNets, which we specialize into continuously (CI) and discretely indexed (DI) collections. On the one hand, we show CI GFlowNets can be interpreted through the lens of a random features expansion, provably boosting the sampler's expressivity in graph-structured tasks and reducing learning instability via spectral shifting. On the other hand, we demonstrate DI GFlowNets encompass prior approaches for GFlowNet training and provide the foundation for the newly proposed Stratum-Conditioned (SC) GFlowNets. This method, which is inspired by the Doob's h-transform of Markov chains, decomposes the state space according to a prescribed modular function and restricts each component to sample from a distinct subset of it. Importantly, SC GFlowNets support centralized and component-wise embarrassingly parallel training, and we show both of them significantly speed up learning convergence and mode coverage without introducing any non-negligible extra computation.

Problem

• GFlowNets
• Mixture of GFlowNets
• Discrete target distribution
• Runtime overhead
• State space exploration

Innovation

• GFlowNets
• Mixture Model
• Random Features Expansion
• Doob's h-transform
• Stratum-Conditioned