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

• URL: http://arxiv.org/abs/2510.18777v1
• Date: Tue, 21 Oct 2025 16:25:19 GMT
• Title: A Frequentist Statistical Introduction to Variational Inference, Autoencoders, and Diffusion Models
• Authors: Yen-Chi Chen,
• Abstract summary: Variational Inference (VI) is central to modern generative models like Variational Autoencoders (VAEs) and Denoising Diffusion Models (DDMs)<n>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.
• Score: 0.7106986689736825
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Variational Inference for Latent Variable Models in High Dimensions [4.3012765978447565]
  We introduce a general framework for quantifying the statistical accuracy of mean-field variational inference (MFVI)<n>We capture the exact regime where MFVI 'works' for the celebrated latent Dirichlet allocation model.<n>Our proof techniques, which extend the framework of nonlinear large deviations, open the door for the analysis of MFVI in other latent variable models.
  arXiv  Detail & Related papers  (2025-06-02T17:19:58Z)
• Recursive Learning of Asymptotic Variational Objectives [49.69399307452126]
  General state-space models (SSMs) are widely used in statistical machine learning and are among the most classical generative models for sequential time-series data. Online sequential IWAE (OSIWAE) allows for online learning of both model parameters and a Markovian recognition model for inferring latent states. This approach is more theoretically well-founded than recently proposed online variational SMC methods.
  arXiv  Detail & Related papers  (2024-11-04T16:12:37Z)
• MMA-DFER: MultiModal Adaptation of unimodal models for Dynamic Facial Expression Recognition in-the-wild [81.32127423981426]
  Multimodal emotion recognition based on audio and video data is important for real-world applications. Recent methods have focused on exploiting advances of self-supervised learning (SSL) for pre-training of strong multimodal encoders. We propose a different perspective on the problem and investigate the advancement of multimodal DFER performance by adapting SSL-pre-trained disjoint unimodal encoders.
  arXiv  Detail & Related papers  (2024-04-13T13:39:26Z)
• Diffusion models for probabilistic programming [56.47577824219207]
  Diffusion Model Variational Inference (DMVI) is a novel method for automated approximate inference in probabilistic programming languages (PPLs) DMVI is easy to implement, allows hassle-free inference in PPLs without the drawbacks of, e.g., variational inference using normalizing flows, and does not make any constraints on the underlying neural network model.
  arXiv  Detail & Related papers  (2023-11-01T12:17:05Z)
• Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEs [50.25683648762602]
  We introduce Koopman VAE, a new generative framework that is based on a novel design for the model prior. Inspired by Koopman theory, we represent the latent conditional prior dynamics using a linear map. KoVAE outperforms state-of-the-art GAN and VAE methods across several challenging synthetic and real-world time series generation benchmarks.
  arXiv  Detail & Related papers  (2023-10-04T07:14:43Z)
• PAVI: Plate-Amortized Variational Inference [55.975832957404556]
  Inference is challenging for large population studies where millions of measurements are performed over a cohort of hundreds of subjects. This large cardinality renders off-the-shelf Variational Inference (VI) computationally impractical. In this work, we design structured VI families that efficiently tackle large population studies.
  arXiv  Detail & Related papers  (2023-08-30T13:22:20Z)
• Amortized Variational Inference: When and Why? [17.1222896154385]
  Amortized variational inference (A-VI) learns a common inference function, which maps each observation to its corresponding latent variable's approximate posterior. We derive conditions on a latent variable model which are necessary, sufficient, and verifiable under which A-VI can attain F-VI's optimal solution.
  arXiv  Detail & Related papers  (2023-07-20T16:45:22Z)
• Amortized Variational Inference: A Systematic Review [0.0]
  The core principle of Variational Inference (VI) is to convert the statistical inference problem of computing complex posterior probability densities into a tractable optimization problem. The traditional VI algorithm is not scalable to large data sets and is unable to readily infer out-of-bounds data points. Recent developments in the field, like black box-, and amortized-VI, have helped address these issues.
  arXiv  Detail & Related papers  (2022-09-22T09:45:10Z)
• Regularizing Variational Autoencoder with Diversity and Uncertainty Awareness [61.827054365139645]
  Variational Autoencoder (VAE) approximates the posterior of latent variables based on amortized variational inference. We propose an alternative model, DU-VAE, for learning a more Diverse and less Uncertain latent space.
  arXiv  Detail & Related papers  (2021-10-24T07:58:13Z)
• An Introduction to Variational Inference [0.0]
  In this paper, we introduce the concept of Variational Inference (VI) VI is a popular method in machine learning that uses optimization techniques to estimate complex probability densities. We discuss the applications of VI to variational auto-encoders (VAE) and VAE-Generative Adversarial Network (VAE-GAN)
  arXiv  Detail & Related papers  (2021-08-30T09:40:04Z)
• Meta-Learning Divergences of Variational Inference [49.164944557174294]
  Variational inference (VI) plays an essential role in approximate Bayesian inference. We propose a meta-learning algorithm to learn the divergence metric suited for the task of interest. We demonstrate our approach outperforms standard VI on Gaussian mixture distribution approximation.
  arXiv  Detail & Related papers  (2020-07-06T17:43:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.