mlsanityData to 14 Oct 2026

Sequential Monte Carlo approximations of Wasserstein--Fisher--Rao gradient flows

arXiv 2506.05905 ↗First posted 6 Jun 2025stat.ME cs.NA math.NAcited by 5

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Abstract (arXiv)

We consider the problem of sampling from a probability distribution π. It is well known that this can be written as an optimisation problem over the space of probability distribution in which we aim to minimise the Kullback--Leibler divergence from π. We consider several partial differential equations (PDEs) whose solution is a minimiser of the Kullback--Leibler divergence from π and connect them to well-known Monte Carlo algorithms. We focus in particular on PDEs obtained by considering the Wasserstein--Fisher--Rao geometry over the space of probabilities and show that these lead to a natural implementation using importance sampling and sequential Monte Carlo. We propose a novel algorithm to approximate the Wasserstein--Fisher--Rao flow of the Kullback--Leibler divergence and conduct an extensive empirical study to identify when these algorithms outperforms other popular Monte Carlo algorithms.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 35 of its 82 references that are in the map. First posted on arXiv 6 Jun 2025.

Builds on

35 of 82 references.

References · 35

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23 more
  1. 2022Birth-death dynamics for sampling: Global convergence, approximations and their asymptoticscited by 30
  2. 2023Learning Gaussian Mixtures Using the Wasserstein-Fisher-Rao Gradient Flowcited by 27
  3. 2024Sampling in Unit Time with Kernel Fisher-Rao Flowcited by 27
  4. 2022Particle algorithms for maximum likelihood training of latent variable modelscited by 26
  5. 2015Provable Bayesian Inference via Particle Mirror Descentcited by 23
  6. 2024Provable Benefit of Annealed Langevin Monte Carlo for Non-log-concave Samplingcited by 23
  7. 2023Sampling via Gradient Flows in the Space of Probability Measurescited by 20
  8. 2019Stochastic Proximal Langevin Algorithm: Potential Splitting and Nonasymptotic Ratescited by 17
  9. 2023Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariancecited by 16
  10. 2023An Explicit Expansion of the Kullback-Leibler Divergence along its Fisher-Rao Gradient Flowcited by 16
  11. 2023A connection between Tempering and Entropic Mirror Descentcited by 16
  12. 2021Adaptive Importance Sampling meets Mirror Descent: a Bias-variance tradeoffcited by 13
  13. 2024Error bounds for particle gradient descent, and extensions of the log-Sobolev and Talagrand inequalitiescited by 13
  14. 2024Fisher-Rao Gradient Flow: Geodesic Convexity and Functional Inequalitiescited by 13
  15. 2024Measure transport with kernel mean embeddingscited by 11
  16. 2024Stein transport for Bayesian inferencecited by 11
  17. 2024Provable Convergence and Limitations of Geometric Tempering for Langevin Dynamicscited by 10
  18. 2024Efficient, Multimodal, and Derivative-Free Bayesian Inference With Fisher-Rao Gradient Flowscited by 9
  19. 2024Connections between sequential Bayesian inference and evolutionary dynamicscited by 4
  20. 2025Evolution of Gaussians in the Hellinger-Kantorovich-Boltzmann gradient flowcited by 3
  21. 2019Collective Proposal Distributions for Nonlinear MCMC samplers: Mean-Field Theory and Fast Implementationcited by 2
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  23. 2023Properties of Marginal Sequential Monte Carlo Methodscited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 3.

5 papers.

  1. 2025A note on the unique properties of the Kullback--Leibler divergence for sampling via gradient flowscited by 4
  2. 2025An operator splitting analysis of Wasserstein--Fisher--Rao gradient flowscited by 2
  3. 2026Properties and limitations of geometric tempering for gradient flow dynamicscited by 0
  4. 2026Preservation of Log-Concavity and Convergence of Wasserstein-Fisher-Rao Gradient Flowscited by 0
  5. 2026Neural Sampling with Reweighted Normalizing Flows via the Wasserstein--Fisher--Rao JKO Schemecited by 0