A Frequentist Statistical Introduction to Variational Inference, Autoencoders, and Diffusion Models

TL;DR

This paper offers a clear, Frequentist perspective on Variational Inference, connecting classical statistical methods with modern deep generative models like VAEs and DDMs, facilitating interdisciplinary understanding.

Contribution

It provides a unified Frequentist explanation of VI, VAEs, and DDMs, bridging the gap between statistical inference and deep learning-based generative models.

Findings

VI as a scalable solution for intractable E-steps

VAEs and DDMs as extensions of the EM algorithm

Bridging statistical inference with deep generative models

Abstract

While Variational Inference (VI) is central to modern generative models like Variational Autoencoders (VAEs) and Denoising Diffusion Models (DDMs), its pedagogical treatment is split across disciplines. In statistics, VI is typically framed as a Bayesian method for posterior approximation. In machine learning, however, VAEs and DDMs are developed from a Frequentist viewpoint, where VI is used to approximate a maximum likelihood estimator. This creates a barrier for statisticians, as the principles behind VAEs and DDMs are hard to contextualize without a corresponding Frequentist introduction to VI. This paper provides that introduction: we explain the theory for VI, VAEs, and DDMs from a purely Frequentist perspective, starting with the classical Expectation-Maximization (EM) algorithm. We show how VI arises as a scalable solution for intractable E-steps and how VAEs and DDMs are natural, deep-learning-based extensions of this framework, thereby bridging the gap between classical statistical inference and modern generative AI.