Variational Potential Flow: A Novel Probabilistic Framework for Energy-Based Generative Modelling

TL;DR

VAPO introduces a new energy-based generative framework that eliminates the need for implicit MCMC sampling, enabling efficient training and realistic image generation by learning a potential energy function guiding prior samples.

Contribution

The paper proposes VAPO, a novel framework that trains energy-based models without implicit MCMC, simplifying training and improving image generation quality.

Findings

Achieves competitive FID scores on CIFAR-10 and CelebA datasets.

Generates realistic images by solving an ODE on a fixed time interval.

Eliminates the need for latent models or cooperative training.

Abstract

Energy based models (EBMs) are appealing for their generality and simplicity in data likelihood modeling, but have conventionally been difficult to train due to the unstable and time-consuming implicit MCMC sampling during contrastive divergence training. In this paper, we present a novel energy-based generative framework, Variational Potential Flow (VAPO), that entirely dispenses with implicit MCMC sampling and does not rely on complementary latent models or cooperative training. The VAPO framework aims to learn a potential energy function whose gradient (flow) guides the prior samples, so that their density evolution closely follows an approximate data likelihood homotopy. An energy loss function is then formulated to minimize the Kullback-Leibler divergence between density evolution of the flow-driven prior and the data likelihood homotopy. Images can be generated after training the potential energy, by initializing the samples from Gaussian prior and solving the ODE governing the potential flow on a fixed time interval using generic ODE solvers. Experiment results show that the proposed VAPO framework is capable of generating realistic images on various image datasets. In particular, our proposed framework achieves competitive FID scores for unconditional image generation on the CIFAR-10 and CelebA datasets.