mlsanityData to 7 Oct 2026

SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence

arXiv 2006.02509 ↗First posted 3 Jun 2020math.ST cs.LG stat.THcited by 64

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Abstract (arXiv)

Stein Variational Gradient Descent (SVGD), a popular sampling algorithm, is often described as the kernelized gradient flow for the Kullback-Leibler divergence in the geometry of optimal transport. We introduce a new perspective on SVGD that instead views SVGD as the (kernelized) gradient flow of the chi-squared divergence which, we show, exhibits a strong form of uniform exponential ergodicity under conditions as weak as a Poincar'e inequality. This perspective leads us to propose an alternative to SVGD, called Laplacian Adjusted Wasserstein Gradient Descent (LAWGD), that can be implemented from the spectral decomposition of the Laplacian operator associated with the target density. We show that LAWGD exhibits strong convergence guarantees and good practical performance.

Key facts. Cited by 64 papers in the map (data through 7 Oct 2026). First posted on arXiv 3 Jun 2020.

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Citing papers per year: 2021: 8; 2022: 10; 2023: 15; 2024: 14; 2025: 10; 2026: 7.

64 papers.

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  1. 2022Variational inference via Wasserstein gradient flowscited by 84
  2. 2021Kernel Stein Discrepancy Descentcited by 57
  3. 2023Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Spacecited by 36
  4. 2022Birth-death dynamics for sampling: Global convergence, approximations and their asymptoticscited by 30
  5. 2022Improving Task-free Continual Learning by Distributionally Robust Memory Evolutioncited by 29
  6. 2024Scalable Wasserstein Gradient Flow for Generative Modeling through Unbalanced Optimal Transportcited by 22
  7. 2021A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1cited by 21
  8. 2021On Stein Variational Neural Network Ensemblescited by 21
  9. 2022Particle-based Variational Inference with Preconditioned Functional Gradient Flowcited by 20
  10. 2023Sampling via Gradient Flows in the Space of Probability Measurescited by 20
  11. 2021Neural Variational Gradient Descentcited by 19
  12. 2024Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusioncited by 19
38 more
  1. 2022Regularized Stein Variational Gradient Flowcited by 18
  2. 2022Sampling with Mollified Interaction Energy Descentcited by 17
  3. 2021Stein Variational Gradient Descent: many-particle and long-time asymptoticscited by 15
  4. 2023Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descentcited by 13
  5. 2024Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descentcited by 13
  6. 2025Wasserstein Policy Optimizationcited by 12
  7. 2024Stein transport for Bayesian inferencecited by 11
  8. 2023Particle-based Variational Inference with Generalized Wasserstein Gradient Flowcited by 10
  9. 2025Weighted quantization using MMD: From mean field to mean shift via gradient flowscited by 10
  10. 2023Coin Sampling: Gradient-Based Bayesian Inference without Learning Ratescited by 8
  11. 2023Minimizing f-Divergences by Interpolating Velocity Fieldscited by 8
  12. 2023Bridging the Gap Between Variational Inference and Wasserstein Gradient Flowscited by 8
  13. 2023A generative flow for conditional sampling via optimal transportcited by 7
  14. 2024Interaction-Force Transport Gradient Flowscited by 7
  15. 2024Kernel Approximation of Fisher-Rao Gradient Flowscited by 7
  16. 2025Hellinger-Kantorovich Gradient Flows: Global Exponential Decay of Entropy Functionalscited by 7
  17. 2022A blob method for inhomogeneous diffusion with applications to multi-agent control and samplingcited by 6
  18. 2023Diffusion map particle systems for generative modelingcited by 6
  19. 2023Provably Fast Finite Particle Variants of SVGD via Virtual Particle Stochastic Approximationcited by 6
  20. 2021Sampling From the Wasserstein Barycentercited by 5
  21. 2023MESSY Estimation: Maximum-Entropy based Stochastic and Symbolic densitY Estimationcited by 5
  22. 2021Multilevel Stein variational gradient descent with applications to Bayesian inverse problemscited by 4
  23. 2023Accelerate Langevin Sampling with Birth-Death Process and Exploration Componentcited by 4
  24. 2024Analysis of Kernel Mirror Prox for Measure Optimizationcited by 4
  25. 2024Wasserstein Gradient Boosting: A Framework for Distribution-Valued Supervised Learningcited by 4
  26. 2024Inclusive KL Gradient Flows: Otto-Wasserstein, Fisher-Rao-Gaussian, and Local-Estimator Dynamicscited by 4
  27. 2025Ultra-fast feature learning for the training of two-layer neural networks in the two-timescale regimecited by 4
  28. 2025A note on the unique properties of the Kullback--Leibler divergence for sampling via gradient flowscited by 4
  29. 2021De-randomizing MCMC dynamics with the diffusion Stein operatorcited by 3
  30. 2023Learning Rate Free Sampling in Constrained Domainscited by 3
  31. 2024Statistical and Geometrical properties of regularized Kernel Kullback-Leibler divergencecited by 3
  32. 2026Finite-Particle Rates for Regularized Stein Variational Gradient Descentcited by 3
  33. 2026Sobolev Regularized MMD Gradient Flowcited by 3
  34. 2022Mean-Field Analysis of Two-Layer Neural Networks: Global Optimality with Linear Convergence Ratescited by 2
  35. 2022NAG-GS: Semi-Implicit, Accelerated and Robust Stochastic Optimizercited by 2
  36. 2023Score Operator Newton transportcited by 1
  37. 2024Semi-Implicit Functional Gradient Flow for Efficient Samplingcited by 1
  38. 2024ELBOing Stein: Variational Bayes with Stein Mixture Inferencecited by 1

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