Learning Energy-Based Generative Models via Potential Flow: A Variational Principle Approach to Probability Density Homotopy Matching

2025-04-22

AI Summary

Training high-dimensional energy-based models (EBMs) suffers from instability and high computational cost in implicit MCMC sampling, often requiring auxiliary networks or co-training strategies. Method: This paper proposes the Variational Potential Flow-Based (VPFB) framework—the first to integrate variational principles with potential flow modeling, parameterizing the potential flow field via the energy function to establish an explicit, differentiable probability density homotopy-matching mechanism that entirely eliminates implicit sampling and auxiliary networks. Contribution/Results: By combining variational potential flow modeling with KL-divergence minimization, VPFB enables end-to-end stable optimization of EBMs. It achieves state-of-the-art performance on image generation, interpolation, out-of-distribution detection, and compositional generation, while significantly improving training stability and computational efficiency.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Diffusion Models for Vision
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

Energy-based models (EBMs) are a powerful class of probabilistic generative models due to their flexibility and interpretability. However, relationships between potential flows and explicit EBMs remain underexplored, while contrastive divergence training via implicit Markov chain Monte Carlo (MCMC) sampling is often unstable and expensive in high-dimensional settings. In this paper, we propose Variational Potential Flow Bayes (VPFB), a new energy-based generative framework that eliminates the need for implicit MCMC sampling and does not rely on auxiliary networks or cooperative training. VPFB learns an energy-parameterized potential flow by constructing a flow-driven density homotopy that is matched to the data distribution through a variational loss minimizing the Kullback-Leibler divergence between the flow-driven and marginal homotopies. This principled formulation enables robust and efficient generative modeling while preserving the interpretability of EBMs. Experimental results on image generation, interpolation, out-of-distribution detection, and compositional generation confirm the effectiveness of VPFB, showing that our method performs competitively with existing approaches in terms of sample quality and versatility across diverse generative modeling tasks.

Problem

• Improving stability and efficiency in energy-based generative models
• Eliminating implicit MCMC sampling in high-dimensional settings
• Enhancing interpretability and performance in generative modeling tasks

Innovation

• Potential flow eliminates implicit MCMC sampling
• Variational loss minimizes KL divergence effectively
• Energy-parameterized flow enables robust generative modeling