Energy Discrepancies: A Score-Independent Loss for Energy-Based Models

TL;DR

This paper introduces Energy Discrepancy, a new loss function for energy-based models that avoids complex score computations, enabling faster and more accurate training especially for low-dimensional data.

Contribution

The paper proposes Energy Discrepancy, a novel loss function that interpolates between score matching and negative log-likelihood, simplifying training of energy-based models.

Findings

ED learns low-dimensional data distributions faster and more accurately.

ED overcomes nearsightedness of score-based methods with theoretical guarantees.

Effective for training energy-based models as priors in high-dimensional image tasks.

Abstract

Energy-based models are a simple yet powerful class of probabilistic models, but their widespread adoption has been limited by the computational burden of training them. We propose a novel loss function called Energy Discrepancy (ED) which does not rely on the computation of scores or expensive Markov chain Monte Carlo. We show that ED approaches the explicit score matching and negative log-likelihood loss under different limits, effectively interpolating between both. Consequently, minimum ED estimation overcomes the problem of nearsightedness encountered in score-based estimation methods, while also enjoying theoretical guarantees. Through numerical experiments, we demonstrate that ED learns low-dimensional data distributions faster and more accurately than explicit score matching or contrastive divergence. For high-dimensional image data, we describe how the manifold hypothesis puts limitations on our approach and demonstrate the effectiveness of energy discrepancy by training the energy-based model as a prior of a variational decoder model.