Hierarchical VAE with a Diffusion-based VampPrior (2412.01373v1)

Abstract: Deep hierarchical variational autoencoders (VAEs) are powerful latent variable generative models. In this paper, we introduce Hierarchical VAE with Diffusion-based Variational Mixture of the Posterior Prior (VampPrior). We apply amortization to scale the VampPrior to models with many stochastic layers. The proposed approach allows us to achieve better performance compared to the original VampPrior work and other deep hierarchical VAEs, while using fewer parameters. We empirically validate our method on standard benchmark datasets (MNIST, OMNIGLOT, CIFAR10) and demonstrate improved training stability and latent space utilization.

• The paper introduces a novel diffusion-based VampPrior for hierarchical VAEs that improves training stability and generative performance.
• It employs amortization techniques with non-trainable transformations to generate pseudoinputs, reducing parameter count and computational inefficiencies.
• Empirical results on MNIST, OMNIGLOT, and CIFAR10 show enhanced model efficiency and stability over traditional deep hierarchical VAEs.

Hierarchical VAE with a Diffusion-based VampPrior: An Expert Overview

The paper presents advancements in the domain of latent variable generative models, specifically focusing on hierarchical Variational Autoencoders (VAEs). It introduces a novel framework, Hierarchical VAE with a Diffusion-based VampPrior, aimed at improving generative performance and training stability in deep hierarchical VAEs while minimizing parameter use.

Research Context

Latent Variable Models (LVMs), particularly VAEs, have shown efficacy in learning data distribution across diverse modalities like images, audio, and molecules by leveraging amortized variational inference. The hierarchical VAEs—such as ResNET VAEs, BIVA, VDVAE, and NVAE—extend this capability by introducing layers of latent variables, achieving state-of-the-art negative log-likelihood (NLL) performance. However, these models often face challenges with training stability. Existing solutions involve techniques like gradient skipping and spectral normalization, which might not address the crux of latent variable structuring and their prior distributions.

Proposed Approach: Diffusion-based VampPrior VAE

The paper proposes an innovative approach to tackle the instability and inefficiency of existing hierarchical VAE methods by focusing on two prime components: the structural arrangement of latent variables and the formulation of priors for those variables. Recognizing the centrality of priors in VAE performance, it extends the previously established VampPrior to be effective in deep hierarchies.

Key contributions include:

1. VampPrior Adaptation: The authors propose a VampPrior-like approximation that can efficiently scale across deep hierarchical layers, employing amortization techniques for pseudoinputs—variables mimicking real data. Diffusion processes are used here to efficiently generate these pseudoinputs, allowing for scalable training while reducing the demand for vast memory resources associated with large $N$ datasets.
2. Introducing Non-trainable Transformations: Utilizing transformations such as the Discrete Cosine Transform (DCT) to generate pseudoinputs, the model bypasses the typical computational inefficiencies present in earlier methods by amortizing the distribution of pseudoinputs, enhancing the scalability of their models.
3. Diffusion-based Prior Incorporation: Diffusion models offer a flexible, hierarchical generative mechanism apt for modeling complex distribution, effectively serving as a substitute for conventional techniques that rely heavily on gradient optimization tricks.

Empirical Validation

The model is evaluated on standard benchmarks, including MNIST, OMNIGLOT, and CIFAR10 datasets. The results demonstrated:

• Improved Performance: The model achieves enhancements in training stability and utilization of latent space over both the original VampPrior and deep hierarchical VAEs, without the need for complex parameter tweaking.
• Efficient Parameter Utilization: By requiring fewer parameters, the method notably reduces the resource burden typically associated with high-performing VAEs.

Implications and Future Directions

The proposed framework aligns with current trends toward more efficient latent variable models. Its calculated leveraging of diffusion processes and expanded VampPrior application supports larger scalability—a necessary evolution given ever-increasing data volumes and complexities. This development inherently bridges the chasm between tractability and scalability with rich latent representations.

The work sets multiple theoretical and practical implications in motion. It opens avenues for advancing generative models to handle even more diverse and high-dimensional data forms. Future research should explore exploring richer transformation techniques and further refining diffusion-based methods to enhance their application in real-time generative tasks, thus broadening their utility across AI.

Overall, this paper delivers a substantial contribution to the ongoing refinement of hierarchical VAEs, specifically by promoting the synergy of diffusion-based generative models with VampPrior principles, marking a notable progression in the pragmatic deployment of generative AI systems.