Ergodic Generative Flows

2025-05-06

AI Summary

Generative Flow Networks (GFNs) face key challenges in continuous-space modeling and imitation learning (IL), including intractable flow matching (FM) loss computation, train-test acyclicity violations, and reliance on explicit reward models. This paper introduces Ergodic Generative Flows (EGFs), a novel framework that constructs provably universal generative models via a finite set of global diffeomorphisms, enabling analytic computation of the FM loss and end-to-end IL without an external reward model. Our contributions are threefold: (1) the first ergodicity-driven generative flow architecture; (2) KL-weakFM loss, the first FM-based objective enabling reward-model-free IL training; and (3) theoretical guarantees on universal approximation and analytic tractability of the FM loss. We validate EGFs on 2D synthetic tasks, NASA spherical data, and goal-conditioned 2D RL benchmarks, demonstrating both empirical effectiveness and feasibility of FM-based learning in continuous domains.

Technology Category

• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Multiagent Systems: Multiagent Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

Abstract

Generative Flow Networks (GFNs) were initially introduced on directed acyclic graphs to sample from an unnormalized distribution density. Recent works have extended the theoretical framework for generative methods allowing more flexibility and enhancing application range. However, many challenges remain in training GFNs in continuous settings and for imitation learning (IL), including intractability of flow-matching loss, limited tests of non-acyclic training, and the need for a separate reward model in imitation learning. The present work proposes a family of generative flows called Ergodic Generative Flows (EGFs) which are used to address the aforementioned issues. First, we leverage ergodicity to build simple generative flows with finitely many globally defined transformations (diffeomorphisms) with universality guarantees and tractable flow-matching loss (FM loss). Second, we introduce a new loss involving cross-entropy coupled to weak flow-matching control, coined KL-weakFM loss. It is designed for IL training without a separate reward model. We evaluate IL-EGFs on toy 2D tasks and real-world datasets from NASA on the sphere, using the KL-weakFM loss. Additionally, we conduct toy 2D reinforcement learning experiments with a target reward, using the FM loss.

Problem

• Address intractability of flow-matching loss in GFNs
• Enable imitation learning without separate reward models
• Extend GFNs to continuous settings with ergodic flows

Innovation

• Ergodic Generative Flows with universal diffeomorphisms
• KL-weakFM loss for imitation learning
• Tractable flow-matching loss in continuous settings