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Stein Variational Gradient Descent as Gradient Flow

arXiv 1704.07520 ↗First posted 25 Apr 2017stat.MLcited by 149

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Abstract (arXiv)

Stein variational gradient descent (SVGD) is a deterministic sampling algorithm that iteratively transports a set of particles to approximate given distributions, based on an efficient gradient-based update that guarantees to optimally decrease the KL divergence within a function space. This paper develops the first theoretical analysis on SVGD, discussing its weak convergence properties and showing that its asymptotic behavior is captured by a gradient flow of the KL divergence functional under a new metric structure induced by Stein operator. We also provide a number of results on Stein operator and Stein's identity using the notion of weak derivative, including a new proof of the distinguishability of Stein discrepancy under weak conditions.

Key facts. Cited by 149 papers in the map (data through 7 Oct 2026). First posted on arXiv 25 Apr 2017.

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Citing papers per year: 2021: 23; 2022: 31; 2023: 32; 2024: 21; 2025: 20; 2026: 22.

149 papers.

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  1. 2021Repulsive Deep Ensembles are Bayesiancited by 103
  2. 2021Priors in Bayesian Deep Learning: A Reviewcited by 101
  3. 2022Variational inference via Wasserstein gradient flowscited by 84
  4. 2021Optimizing Functionals on the Space of Probabilities with Input Convex Neural Networkscited by 53
  5. 2022Probability flow solution of the Fokker-Planck equationcited by 46
  6. 2022Understanding and Mitigating Overfitting in Prompt Tuning for Vision-Language Modelscited by 40
  7. 2021KALE Flow: A Relaxed KL Gradient Flow for Probabilities with Disjoint Supportcited by 37
  8. 2023Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Spacecited by 36
  9. 2023Generative Sliced MMD Flows with Riesz Kernelscited by 36
  10. 2023A Rigorous Link between Deep Ensembles and (Variational) Bayesian Methodscited by 31
  11. 2022Birth-death dynamics for sampling: Global convergence, approximations and their asymptoticscited by 30
  12. 2022Improving Task-free Continual Learning by Distributionally Robust Memory Evolutioncited by 29
38 more
  1. 2022BaCaDI: Bayesian Causal Discovery with Unknown Interventionscited by 26
  2. 2024DreamFlow: High-Quality Text-to-3D Generation by Approximating Probability Flowcited by 26
  3. 2021Projected Wasserstein gradient descent for high-dimensional Bayesian inferencecited by 24
  4. 2023SteinDreamer: Variance Reduction for Text-to-3D Score Distillation via Stein Identitycited by 23
  5. 2022A Finite-Particle Convergence Rate for Stein Variational Gradient Descentcited by 22
  6. 2021A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1cited by 21
  7. 2021On Stein Variational Neural Network Ensemblescited by 21
  8. 2021Efficient Gradient Flows in Sliced-Wasserstein Spacecited by 21
  9. 2023Unifying GANs and Score-Based Diffusion as Generative Particle Modelscited by 21
  10. 2022Particle-based Variational Inference with Preconditioned Functional Gradient Flowcited by 20
  11. 2023Sampling via Gradient Flows in the Space of Probability Measurescited by 20
  12. 2021Neural Variational Gradient Descentcited by 19
  13. 2024Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusioncited by 19
  14. 2022Regularized Stein Variational Gradient Flowcited by 18
  15. 2024S2AC: Energy-Based Reinforcement Learning with Stein Soft Actor Criticcited by 18
  16. 2021Sampling with Mirrored Stein Operatorscited by 17
  17. 2021Probabilistic Inference of Simulation Parameters via Parallel Differentiable Simulationcited by 17
  18. 2022Sampling with Mollified Interaction Energy Descentcited by 17
  19. 2026Generative Drifting is Secretly Score Matching: a Spectral and Variational Perspectivecited by 17
  20. 2022Convergence of Stein Variational Gradient Descent under a Weaker Smoothness Conditioncited by 16
  21. 2023Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariancecited by 16
  22. 2023A connection between Tempering and Entropic Mirror Descentcited by 16
  23. 2021Wasserstein Proximal of GANscited by 15
  24. 2021Stein Variational Gradient Descent: many-particle and long-time asymptoticscited by 15
  25. 2022Targeted Separation and Convergence with Kernel Discrepanciescited by 15
  26. 2024Repulsive Latent Score Distillation for Solving Inverse Problemscited by 15
  27. 2023Label-Efficient Deep Learning in Medical Image Analysis: Challenges and Future Directionscited by 14
  28. 2023Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descentcited by 13
  29. 2024Nonparametric Teaching of Implicit Neural Representationscited by 13
  30. 2024Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descentcited by 13
  31. 2022Toward Equation of Motion for Deep Neural Networks: Continuous-time Gradient Descent and Discretization Error Analysiscited by 12
  32. 2022Sampling in Constrained Domains with Orthogonal-Space Variational Gradient Descentcited by 11
  33. 2023Tuning-Free Maximum Likelihood Training of Latent Variable Models via Coin Bettingcited by 11
  34. 2024Stein transport for Bayesian inferencecited by 11
  35. 2024Annealing Flow Generative Models Towards Sampling High-Dimensional and Multi-Modal Distributionscited by 11
  36. 2021Learning by example: fast reliability-aware seismic imaging with normalizing flowscited by 10
  37. 2023Dynamic Flows on Curved Space Generated by Labeled Datacited by 10
  38. 2023Particle-based Variational Inference with Generalized Wasserstein Gradient Flowcited by 10

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