mlsanityData to 7 Oct 2026

Sampling in Unit Time with Kernel Fisher-Rao Flow

arXiv 2401.03892 ↗First posted 8 Jan 2024stat.CO cs.LG stat.MLcited by 27

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Abstract (arXiv)

We introduce a new mean-field ODE and corresponding interacting particle systems (IPS) for sampling from an unnormalized target density. The IPS are gradient-free, available in closed form, and only require the ability to sample from a reference density and compute the (unnormalized) target-to-reference density ratio. The mean-field ODE is obtained by solving a Poisson equation for a velocity field that transports samples along the geometric mixture of the two densities, which is the path of a particular Fisher-Rao gradient flow. We employ a RKHS ansatz for the velocity field, which makes the Poisson equation tractable and enables discretization of the resulting mean-field ODE over finite samples. The mean-field ODE can be additionally be derived from a discrete-time perspective as the limit of successive linearizations of the Monge-Amp`ere equations within a framework known as sample-driven optimal transport. We introduce a stochastic variant of our approach and demonstrate empirically that our IPS can produce high-quality samples from varied target distributions, outperforming comparable gradient-free particle systems and competitive with gradient-based alternatives.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). Builds on 35 of its 82 references that are in the map. First posted on arXiv 8 Jan 2024.

Builds on

35 of 82 references.

References · 35

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  2. 2022Flow Matching for Generative Modelingcited by 5,426
  3. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,550
  4. 2015Variational Inference with Normalizing Flowscited by 2,161
  5. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  6. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  7. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  8. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 498
  9. 2023Denoising Diffusion Samplerscited by 144
  10. 2017Measuring Sample Quality with Kernelscited by 119
  11. 2021Annealed Flow Transport Monte Carlocited by 90
  12. 2019On the geometry of Stein variational gradient descentcited by 82
23 more
  1. 2019Sum-of-Squares Polynomial Flowcited by 62
  2. 2022Supervised Training of Conditional Monge Mapscited by 60
  3. 2023Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimizationcited by 57
  4. 2019Coupling techniques for nonlinear ensemble filteringcited by 48
  5. 2017Inference via low-dimensional couplingscited by 43
  6. 2020On the representation and learning of monotone triangular transport mapscited by 41
  7. 2020Conditional Sampling with Monotone GANs: from Generative Models to Likelihood-Free Inferencecited by 40
  8. 2020Sliced Iterative Normalizing Flowscited by 37
  9. 2019Projected Stein Variational Newton: A Fast and Scalable Bayesian Inference Method in High Dimensionscited by 21
  10. 2023Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariancecited by 16
  11. 2023An Explicit Expansion of the Kullback-Leibler Divergence along its Fisher-Rao Gradient Flowcited by 16
  12. 2023A connection between Tempering and Entropic Mirror Descentcited by 16
  13. 2021Adaptive Importance Sampling meets Mirror Descent: a Bias-variance tradeoffcited by 13
  14. 2022An Optimal Transport Formulation of Bayes' Law for Nonlinear Filtering Algorithmscited by 11
  15. 2022MixFlows: principled variational inference via mixed flowscited by 11
  16. 2014Poisson's equation in nonlinear filteringcited by 10
  17. 2021Scalable Bayesian transport maps for high-dimensional non-Gaussian spatial fieldscited by 9
  18. 2022Ensemble transport smoothing. Part II: Nonlinear updatescited by 8
  19. 2023Adaptive Annealed Importance Sampling with Constant Rate Progresscited by 7
  20. 2020Annealed Importance Sampling with q-Pathscited by 6
  21. 2019Sequential Ensemble Transform for Bayesian Inverse Problemscited by 4
  22. 2023A Survey of Feedback Particle Filter and related Controlled Interacting Particle Systems (CIPS)cited by 4
  23. 2019Transform-based particle filtering for elliptic Bayesian inverse problemscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 12; 2025: 11; 2026: 4.

27 papers.

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  1. 2025Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Expertscited by 85
  2. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  3. 2024Fisher-Rao Gradient Flow: Geodesic Convexity and Functional Inequalitiescited by 13
  4. 2024Stein transport for Bayesian inferencecited by 11
  5. 2024Annealing Flow Generative Models Towards Sampling High-Dimensional and Multi-Modal Distributionscited by 11
  6. 2024Provable Convergence and Limitations of Geometric Tempering for Langevin Dynamicscited by 10
  7. 2025Weighted quantization using MMD: From mean field to mean shift via gradient flowscited by 10
  8. 2024Efficient, Multimodal, and Derivative-Free Bayesian Inference With Fisher-Rao Gradient Flowscited by 9
  9. 2024Path-Guided Particle-based Samplingcited by 8
  10. 2024Kernel Approximation of Fisher-Rao Gradient Flowscited by 7
  11. 2025Telegrapher's Generative Model via Kac Flowscited by 7
  12. 2025DICE: Discrete inverse continuity equation for learning population dynamicscited by 6
15 more
  1. 2025Sequential Monte Carlo approximations of Wasserstein--Fisher--Rao gradient flowscited by 5
  2. 2024Ensemble-Based Annealed Importance Samplingcited by 4
  3. 2024Inclusive KL Gradient Flows: Otto-Wasserstein, Fisher-Rao-Gaussian, and Local-Estimator Dynamicscited by 4
  4. 2024Connections between sequential Bayesian inference and evolutionary dynamicscited by 4
  5. 2025Score-based deterministic density samplingcited by 4
  6. 2025A note on the unique properties of the Kullback--Leibler divergence for sampling via gradient flowscited by 4
  7. 2025An operator splitting analysis of Wasserstein--Fisher--Rao gradient flowscited by 2
  8. 2024Sequential transport maps using SoS density estimation and α-divergencescited by 1
  9. 2025Learning Paths for Dynamic Measure Transport: A Control Perspectivecited by 1
  10. 2026To discretize continually: Mean shift interacting particle systems for Bayesian inferencecited by 1
  11. 2024Subspace Langevin Monte Carlocited by 0
  12. 2025Guiding Time-Varying Generative Models with Natural Gradients on Exponential Family Manifoldcited by 0
  13. 2026Generative Modeling via Kernelized Stochastic Interpolantscited by 0
  14. 2026Preservation of Log-Concavity and Convergence of Wasserstein-Fisher-Rao Gradient Flowscited by 0
  15. 2026Interacting particle guidance for sampling reward-tilted generative priorscited by 0