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

Junn Yong Loo, Julia K. Lau, Chee-Ming Ting, VISHNU MONN BASKARAN, Raphael CW Phan, Chee Pin Tan

Keywords: generative models, energy-based models, variational methods, particle filtering

TL;DR: In this paper, we present a novel energy-based generative framework called Variational Potential Flow (VAPO).

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 SDE governing the potential flow. 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.

Primary Area: generative models

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.

Reciprocal Reviewing: I understand the reciprocal reviewing requirement as described on https://iclr.cc/Conferences/2025/CallForPapers. If none of the authors are registered as a reviewer, it may result in a desk rejection at the discretion of the program chairs. To request an exception, please complete this form at https://forms.gle/Huojr6VjkFxiQsUp6.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 6001