mlsanityData to 7 Oct 2026

Variational inference via Wasserstein gradient flows

arXiv 2205.15902 ↗First posted 31 May 2022stat.ML cs.LG math.STcited by 84

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Abstract (arXiv)

Along with Markov chain Monte Carlo (MCMC) methods, variational inference (VI) has emerged as a central computational approach to large-scale Bayesian inference. Rather than sampling from the true posterior π, VI aims at producing a simple but effective approximation hat π to π for which summary statistics are easy to compute. However, unlike the well-studied MCMC methodology, algorithmic guarantees for VI are still relatively less well-understood. In this work, we propose principled methods for VI, in which hat π is taken to be a Gaussian or a mixture of Gaussians, which rest upon the theory of gradient flows on the Bures--Wasserstein space of Gaussian measures. Akin to MCMC, it comes with strong theoretical guarantees when π is log-concave.

Key facts. Cited by 84 papers in the map (data through 7 Oct 2026). Builds on 31 of its 98 references that are in the map. First posted on arXiv 31 May 2022.

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31 of 98 references.

References · 31

  1. 2016Variational Inference: A Review for Statisticianscited by 1,466
  2. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 498
  3. 2013Black Box Variational Inferencecited by 317
  4. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
  5. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 206
  6. 2017Stein Variational Gradient Descent as Gradient Flowcited by 149
  7. 2015Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measurescited by 138
  8. 2018Analysis of Langevin Monte Carlo via convex optimizationcited by 126
  9. 2018Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problemcited by 123
  10. 2015On the properties of variational approximations of Gibbs posteriorscited by 121
  11. 2021The Bayesian Learning Rulecited by 95
  12. 2017Noisy Natural Gradient as Variational Inferencecited by 94
19 more
  1. 2020Structured Logconcave Sampling with a Restricted Gaussian Oraclecited by 85
  2. 2019On the geometry of Stein variational gradient descentcited by 82
  3. 2019The Randomized Midpoint Method for Log-Concave Samplingcited by 77
  4. 2019A Wasserstein-type distance in the space of Gaussian Mixture Modelscited by 75
  5. 2017Concentration of tempered posteriors and of their variational approximationscited by 66
  6. 2020SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergencecited by 64
  7. 2018On sampling from a log-concave density using kinetic Langevin diffusionscited by 61
  8. 2017Frequentist Consistency of Variational Bayescited by 60
  9. 2019Fast mixing of Metropolized Hamiltonian Monte Carlo: Benefits of multi-step gradientscited by 51
  10. 2019Fast and Simple Natural-Gradient Variational Inference with Mixture of Exponential-family Approximationscited by 51
  11. 2017Optimal transport for Gaussian mixture modelscited by 45
  12. 2019Accelerating Langevin Sampling with Birth-deathcited by 45
  13. 2021Minimax Mixing Time of the Metropolis-Adjusted Langevin Algorithm for Log-Concave Samplingcited by 44
  14. 2021Averaging on the Bures-Wasserstein manifold: dimension-free convergence of gradient descentcited by 32
  15. 2019Provable Smoothness Guarantees for Black-Box Variational Inferencecited by 29
  16. 2019Stein's Lemma for the Reparameterization Trick with Exponential Family Mixturescited by 18
  17. 2021The computational asymptotics of Gaussian variational inference and the Laplace approximationcited by 8
  18. 2021Mixture weights optimisation for Alpha-Divergence Variational Inferencecited by 6
  19. 2022A blob method for inhomogeneous diffusion with applications to multi-agent control and samplingcited by 6

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Citing papers per year: 2022: 5; 2023: 26; 2024: 16; 2025: 22; 2026: 15.

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  1. 2023Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Spacecited by 36
  2. 2023Convergence of flow-based generative models via proximal gradient descent in Wasserstein spacecited by 34
  3. 2022Birth-death dynamics for sampling: Global convergence, approximations and their asymptoticscited by 30
  4. 2023Provable convergence guarantees for black-box variational inferencecited by 29
  5. 2024Wasserstein Flow Matching: Generative modeling over families of distributionscited by 27
  6. 2023Learning Gaussian Mixtures Using the Wasserstein-Fisher-Rao Gradient Flowcited by 25
  7. 2023On the Convergence of Black-Box Variational Inferencecited by 22
  8. 2024Batch and match: black-box variational inference with a score-based divergencecited by 22
  9. 2023Sampling via Gradient Flows in the Space of Probability Measurescited by 20
  10. 2023Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein spacecited by 20
  11. 2022Mean-field Variational Inference via Wasserstein Gradient Flowcited by 19
  12. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
38 more
  1. 2023Projected Langevin dynamics and a gradient flow for entropic optimal transportcited by 17
  2. 2023An Explicit Expansion of the Kullback-Leibler Divergence along its Fisher-Rao Gradient Flowcited by 16
  3. 2024Repulsive Latent Score Distillation for Solving Inverse Problemscited by 15
  4. 2023Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descentcited by 13
  5. 2024Convergence of coordinate ascent variational inference for log-concave measures via optimal transportcited by 13
  6. 2023Independent projections of diffusions: Gradient flows for variational inference and optimal mean field approximationscited by 12
  7. 2023Momentum Particle Maximum Likelihoodcited by 12
  8. 2024Theoretical Guarantees for Variational Inference with Fixed-Variance Mixture of Gaussianscited by 11
  9. 2023Accelerating optimization over the space of probability measurescited by 9
  10. 2024Efficient, Multimodal, and Derivative-Free Bayesian Inference With Fisher-Rao Gradient Flowscited by 9
  11. 2024Variational Inference in Location-Scale Families: Exact Recovery of the Mean and Correlation Matrixcited by 9
  12. 2023Bridging the Gap Between Variational Inference and Wasserstein Gradient Flowscited by 8
  13. 2022Statistical and Computational Trade-offs in Variational Inference: A Case Study in Inferential Model Selectioncited by 7
  14. 2024Sampling from the Mean-Field Stationary Distributioncited by 7
  15. 2024Particle Semi-Implicit Variational Inferencecited by 7
  16. 2024Importance Corrected Neural JKO Samplingcited by 7
  17. 2025Hellinger-Kantorovich Gradient Flows: Global Exponential Decay of Entropy Functionalscited by 7
  18. 2023Bures-Wasserstein Means of Graphscited by 6
  19. 2025Learning of Population Dynamics: Inverse Optimization Meets JKO Schemecited by 6
  20. 2025Variational Inference with Mixtures of Isotropic Gaussianscited by 6
  21. 2023VITS : Variational Inference Thompson Sampling for contextual banditscited by 5
  22. 2023Wasserstein Gradient Flow over Variational Parameter Space for Variational Inferencecited by 5
  23. 2024Non-geodesically-convex optimization in the Wasserstein spacecited by 5
  24. 2025Sequential Monte Carlo approximations of Wasserstein--Fisher--Rao gradient flowscited by 5
  25. 2025Are We Really Learning the Score Function? Reinterpreting Diffusion Models Through Wasserstein Gradient Flow Matchingcited by 5
  26. 2023Particle Mean Field Variational Bayescited by 4
  27. 2023Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithmscited by 4
  28. 2023A Mean Field Approach to Empirical Bayes Estimation in High-dimensional Linear Regressioncited by 4
  29. 2023Gromov-Wasserstein-like Distances in the Gaussian Mixture Models Spacecited by 4
  30. 2024Inclusive KL Gradient Flows: Otto-Wasserstein, Fisher-Rao-Gaussian, and Local-Estimator Dynamicscited by 4
  31. 2025Training Latent Diffusion Models with Interacting Particle Algorithmscited by 4
  32. 2025A note on the unique properties of the Kullback--Leibler divergence for sampling via gradient flowscited by 4
  33. 2023Wasserstein PAC-Bayes Learning: Exploiting Optimisation Guarantees to Explain Generalisationcited by 3
  34. 2023Approximation properties of slice-matching operatorscited by 3
  35. 2024A Particle Algorithm for Mean-Field Variational Inferencecited by 3
  36. 2025Evolution of Gaussians in the Hellinger-Kantorovich-Boltzmann gradient flowcited by 3
  37. 2025Optimization Guarantees for Square-Root Natural-Gradient Variational Inferencecited by 3
  38. 2022NAG-GS: Semi-Implicit, Accelerated and Robust Stochastic Optimizercited by 2

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