VAEBM: A Symbiosis between Variational Autoencoders and Energy-based Models (2010.00654v3)

Abstract: Energy-based models (EBMs) have recently been successful in representing complex distributions of small images. However, sampling from them requires expensive Markov chain Monte Carlo (MCMC) iterations that mix slowly in high dimensional pixel space. Unlike EBMs, variational autoencoders (VAEs) generate samples quickly and are equipped with a latent space that enables fast traversal of the data manifold. However, VAEs tend to assign high probability density to regions in data space outside the actual data distribution and often fail at generating sharp images. In this paper, we propose VAEBM, a symbiotic composition of a VAE and an EBM that offers the best of both worlds. VAEBM captures the overall mode structure of the data distribution using a state-of-the-art VAE and it relies on its EBM component to explicitly exclude non-data-like regions from the model and refine the image samples. Moreover, the VAE component in VAEBM allows us to speed up MCMC updates by reparameterizing them in the VAE's latent space. Our experimental results show that VAEBM outperforms state-of-the-art VAEs and EBMs in generative quality on several benchmark image datasets by a large margin. It can generate high-quality images as large as 256$\times$256 pixels with short MCMC chains. We also demonstrate that VAEBM provides complete mode coverage and performs well in out-of-distribution detection. The source code is available at https://github.com/NVlabs/VAEBM

• The paper introduces VAEBM, a hybrid model that combines the fast sampling of VAEs with the precise mode refinement of EBMs.
• It leverages latent space MCMC updates to accelerate mixing and generate sharper images with complete mode coverage.
• Empirical results on CIFAR-10 and CelebA HQ show improved performance with an IS of 8.43 and an FID of 12.19, ensuring effective out-of-distribution detection.

An Overview of "VAEBM: A Symbiosis between Variational Autoencoders and Energy-based Models"

The paper "VAEBM: A Symbiosis between Variational Autoencoders and Energy-based Models" introduces an innovative approach to generative modeling by combining two prominent architectures: Variational Autoencoders (VAEs) and Energy-Based Models (EBMs). The objective here is to leverage the complementary strengths of both models to improve generative performance on image datasets.

Core Contributions

The paper proposes VAEBM, a hybrid model that integrates the fast sampling capabilities of VAEs with the precise mode coverage of EBMs. This novel composition aims to address prevalent issues in both architectures individually: VAEs often sample from improbable regions of the data space and generate less sharp images, while EBMs tend to suffer from high computational costs and slow mixing due to reliance on Markov Chain Monte Carlo (MCMC) iterations for image sampling.

The synergy in VAEBM brings forth the following functionalities:

• Balancing Mode Structure and Sample Refinement: The VAE component captures the overall mode structure of the data distribution. The EBM component, on the other hand, focuses on refining the generated samples by identifying and penalizing non-data-like regions, thereby ensuring mode fidelity and eliminating spurious modes.
• Efficient MCMC Sampling in Latent Space: VAEBM employs the VAE's latent space for reparameterizing MCMC updates, which accelerates the mixing rate and reduces the required number of MCMC steps, allowing the model to generate high-quality images faster.

Empirical Evaluation

In a series of experiments across several benchmark datasets, including CIFAR-10 and CelebA HQ with sizes up to 256×256 pixels, VAEBM demonstrates superior performance compared to standalone VAEs and EBMs. Specifically, in the CIFAR-10 dataset, VAEBM achieves an Inception Score (IS) of 8.43 and an FID of 12.19, outperforming established EBM and VAE-based approaches. Additionally, the model maintains complete mode coverage and effectively identifies out-of-distribution data, a challenging task for many generative models.

Implications and Future Directions

The VAEBM framework has substantial theoretical implications, as it bridges the gap between likelihood-based models and adversarial networks by offering stable training and robust out-of-distribution detection. Practically, this advancement in generative modeling enhances applications in image synthesis, anomaly detection, and possibly extends to complex multimodal data.

From a future research perspective, the paper opens the path for exploring alternative sampling strategies to further enhance the efficiency of VAEBM, particularly when scaling to higher-dimensional data. There is also potential in examining its extension to other domains beyond image data, such as audio and molecular modeling, where the benefits of efficient sampling and mode fidelity are highly desirable.

The combination of VAE and EBM architectures into a unified model, as demonstrated with VAEBM, exemplifies how cross-pollination between different modeling paradigms in machine learning can yield robust solutions and set the stage for ongoing developments in the field of generative models.