Variational Inference

Also known as VI

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Overview

Variational inference turns Bayesian posterior estimation into an optimization problem, fitting a tractable distribution to approximate a typically intractable target. Common approaches include mean-field and structured coordinate ascent, stochastic-gradient ELBO optimization, amortized inference with neural networks and normalizing flows, and particle methods such as Stein variational gradient descent. These methods are used in settings from Gaussian processes and time-series models to deep learning and Bayesian inverse problems, where they can make uncertainty estimates practical at scale. A central tension is that faster, simpler approximations can miss posterior dependencies or modes and miscalibrate uncertainty, motivating more expressive families alongside stronger convergence and calibration guarantees.

Latest papers

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153 papers16 papers in the last four weeks, up 78% on the four weeks before. 0.1% of all new papers.

  1. Gibbs Variational Last Layers for Long-Horizon Dynamics Learning

    Nov 2, 2026Paul Brunzema, Henrik Hose, Sebastian TrimpeProbabilistic Time Series ForecastingBayesian Neural Networks

    RWTH Aachen University, Aachen, Germany

  2. VESPER: Online Learning of Free Energies with a Multi-Tempered Variational Objective

    Oct 30, 2026Jay L. Kaplan, Gustavo R. Pérez-Lemus, Mengjian Hua +2Free Energy CalculationMolecular Dynamics Simulation

    Courant Institute School of Mathematics, Computing, and Data Science, New York University, New York, NY 10012, USA · Department of Chemical and Biomolecular Engineering, Tandon School of Engineering, New York University, Brooklyn, NY 11201, USA · Department of Physics, New York University, New York, NY 10012, USA +1

  3. Rènyi-Regularized Flow-Based Variational Inference for Bayesian Calibration

    Oct 27, 2026Exaucè Luweh Adjim Ngarti, Élise Arnaud, Léo Nicoletti +2Variational InferenceBayesian Inference

    AIRSEA · Mines Saint-Étienne MSE, LIMOS, FAYOL-ENSMSE, FAYOL-ENSMSE

  4. The Bayesian Learning Rule Beyond KL Geometry

    Oct 22, 2026Sophia Sklaviadis, Wu Lin, Andre Martins +3Bayesian InferenceVariational Inference

    Instituto de Telecomunicações and Instituto Superior Técnico, Universidade de Lisboa, Portugal · University of Central Florida, USA · RIKEN Center for Advanced Intelligence Project, Japan +1

  5. Parameter Learning in Active Inference via Variational Message Passing

    Oct 22, 2026Benedikt WaldeckActive InferenceModel-Based Planning

    University of Modena and Reggio Emilia, Italy

  6. Parallelizable Probabilistic Latent Reasoning for Diverse Reasoning Trajectories

    Oct 21, 2026Seokhyun Lee, Seongjun Lee, Changhee LeeContinuous Latent ReasoningReasoning Diversity

    Korea University

  7. Geometry-Aware Block Selection for Sparse Variational Gaussian Processes

    Oct 20, 2026Matteo HoxhaSparse Gaussian ProcessesGaussian Process Regression

    Nanyang Technological University, Singapore

  8. VampPrior Unleashed

    Oct 19, 2026Andrew A. Stirn, Abhejit Rajagopal, David A. Knowles +1Variational InferenceUnsupervised Clustering

    Allen Institute · New York Genome Center & Columbia University

  9. Denoising Implicit Variational Inference

    Oct 17, 2026Zitong Wang, Zekun Wu, Longlin Yu +1Variational InferenceBayesian Inference

    School of Mathematical Sciences, Peking University

  10. Acceleration and its Limits in Gaussian Variational Inference

    Oct 14, 2026Jaesung R. Park, Uijeong Jang, Yifan ChenOracle ComplexityVariational Inference

    Department of Mathematics, University of California, Los Angeles

  11. Implicit and explicit reparameterizations of the Folded Normal and Rice distributions

    Oct 12, 2026Luis Aldama, Kevin Dalton, Minhuan Li +1Variational Inference

    The Harvard Biophysics Graduate Program, Harvard University, Cambridge, Massachusetts, United States · Department of Molecular and Cellular Biology, and John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts, United States · LCLS Data Systems, SLAC National Accelerator Laboratory, Menlo Park, CA 94025. +1

  12. Amortized Variational Inference of Latent Intensities from Replicated Point Patterns

    Oct 12, 2026Wenqing Liu, Xenia Miscouridou, Déborah SulemAmortized InferenceVariational Inference

    Faculty of Informatics, Università della Svizzera italiana, Lugano, Switzerland · Department of Mathematics and Statistics, University of Cyprus, Nicosia, Cyprus

  13. Scalable Sparse Autoregressive Variational Inference for Non-Gaussian Spatial Fields

    Oct 9, 2026Paul F. V. Wiemann, Matthias KatzfussVariational Inference

    Department of Statistics, The Ohio State University, Columbus OH 43210, USA · Department of Statistics, University of Wisconsin–Madison, Madison WI 53706, USA

  14. Scan-Parallel Variational Inference for event-driven Latent Jump Models

    Oct 9, 2026Vansh Bansal, Min Chen, James G. ScottState Space ModelsIrregular Time-Series Modeling

    Department of Statistics and Data Science UT Austin

  15. The Impact of Likelihood Tempering on the Limiting Predictive Moments of Variational Bayesian Linear Neural Networks

    Oct 6, 2026Ian Zhang, Thibault RandrianarisoaBayesian Neural NetworksVariational Inference

    Department of Statistical Sciences, University of Toronto · Dunlap Institute for Astronomy and Astrophysics

  16. Generalized Matheron Variational Implicit Processes

    Oct 6, 2026Luis A. Ortega, Andrés R. Masegosa, Thomas D. NielsenBayesian InferenceGaussian Processes

    Aalborg University

  17. Latent Similarity Gaussian Processes: A Theory-Grounded Approach to Personalized Suicide-Risk Forecasting for Clinical Decision-Support

    Oct 5, 2026Yaniv Yacoby, Weiwei Pan, Hope Neveux +4Latent Variable ModelsSuicide Risk Modeling

    Wellesley College · Harvard University · Harvard University Harvard Medical School Massachusetts General Hospital

  18. Gaussian Flow Dynamics: Simulation-Free Neural SDE Learning Beyond One-Time Marginals

    Oct 3, 2026Grigory Bartosh, Christian A. NaessethStochastic Differential EquationsLatent Dynamics Modeling

    Informatics Institute University of Amsterdam

  19. Amortized Structured Stochastic Variational Inference for Gaussian Process Latent Variable Models

    Oct 2, 2026Maksym Tretiakov, Sarah Filippi, Vincent Fortuin +3Latent Variable ModelsAmortized Inference

    LMU Munich · Munich Center for Machine Learning (MCML) · Imperial College London +3

  20. To Explore The Strange New World Beyond Data Distribution: System Behavior, Causality Tax, and Non-causal Base Model

    Oct 2, 2026Xianzhi Zeng, Jiangneng Li, Gao CongCausal Reasoning in Language ModelsVariational Inference

    College of Computing and Data Science Nanyang Technological University Singapore, 639798

  21. QuanVI: Score-based Variational Inference via Quantum Maximally Mixed States

    Sep 30, 2026Yuchen Cong, Zerui Tao, Chao Li +2Bayesian InferenceQuantum-Inspired ML

    Juntendo University · RIKEN-AIP

  22. Variational Mixtures and Multi-Marginal Flow Matching: Advancing Statistical Inference with Biological Applications

    Sep 29, 2026Oskar KvimanVariational InferenceFlow Matching

    kth royal institute of technology

  23. Simulation-Free Learning of GP-SDEs from Irregular Observations

    Sep 27, 2026Zhidi Lin, Yuhao Liu, Ying Li +2Stochastic Differential EquationsState Space Models

    The University of Hong Kong · Capital One · National University of Singapore +1

  24. DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecasting

    Sep 26, 2026Weiwei Ye, Dongyuan Li, Hangchen Liu +3Time Series ForecastingProbabilistic Time Series Forecasting

    The University of Tokyo · Harbin Institute of Technology, Shenzhen

  25. PR-Smoother: Simulator-Preserving Non-Gaussian Smoothing for Data Assimilation

    Sep 22, 2026Yuta TarumiAmortized InferenceData Assimilation

    iTHEMS RIKEN Kobe, Japan

  26. Variational objectives for amortized Bayesian inference in inverse problems: The role of posterior conditioning

    Sep 21, 2026Abhishek Srivastava, Arijit Hazra, Rajesh DubbakuAmortized InferenceBayesian Inverse Problems

    Department of Mechanical Engineering, Indian Institute of Technology Palakkad · Department of Mathematics, Indian Institute of Technology Palakkad

  27. Theoretical Study on the Evidential Learning-based Variational Autoencoder

    Aug 19, 2026Ge WangQuery IdentifiabilityVariational Autoencoders

    Rensselaer Polytechnic Institute, Troy, New York, USA

  28. Information Geometry of Message Passing

    Aug 16, 2026Mykola Lukashchuk, Kyrylo Yemets, Alex Ledbetter +1Belief PropagationProbabilistic Graphical Models

    Eindhoven University of Technology · Lviv Polytechnic National University · Lazy Dynamics, Utrecht, the Netherlands

  29. Beyond Independence: Learning Correlated Views for Variational Incomplete Multi-View Clustering

    Aug 16, 2026Zheming Xu, Aiyue Tang, Shidi Chen +4Multi-View ClusteringMulti-View Learning

    School of Computer Science & Technology, Beijing Jiaotong University · Key Laboratory of Big Data & Artificial Intelligence in Transportation, Ministry of Education, China · Department of Data Science, BI Norwegian Business School, Oslo, Norway +2

  30. Variational Parameter Calibration with Physics-Aware Latent-Space Surrogates

    Aug 11, 2026Qiyao Zhou, Xujia Zhu, Pierre Joli +2Neural Surrogate ModelingParameter Estimation

    LMEE, UnivEvry, Université Paris-Saclay, Evry, France · L2S, Université Paris-Saclay, CNRS, CentraleSupéléc, Gif-sur-Yvette, France · CEREA, ENPC, EDF R&D, Institut Polytechnique de Paris, Île-de-France, France