mlsanityData to 14 Oct 2026

Liouville Flow Importance Sampler

arXiv 2405.06672 ↗First posted 3 May 2024stat.ML cs.LG math.PRcited by 25

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Abstract (arXiv)

We present the Liouville Flow Importance Sampler (LFIS), an innovative flow-based model for generating samples from unnormalized density functions. LFIS learns a time-dependent velocity field that deterministically transports samples from a simple initial distribution to a complex target distribution, guided by a prescribed path of annealed distributions. The training of LFIS utilizes a unique method that enforces the structure of a derived partial differential equation to neural networks modeling velocity fields. By considering the neural velocity field as an importance sampler, sample weights can be computed through accumulating errors along the sample trajectories driven by neural velocity fields, ensuring unbiased and consistent estimation of statistical quantities. We demonstrate the effectiveness of LFIS through its application to a range of benchmark problems, on many of which LFIS achieved state-of-the-art performance.

Key facts. Cited by 25 papers in the map (data through 14 Oct 2026). Builds on 18 of its 60 references that are in the map. First posted on arXiv 3 May 2024.

Builds on

18 of 60 references.

References · 18

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  2. 2022Flow Matching for Generative Modelingcited by 5,702
  3. 2018Neural Ordinary Differential Equationscited by 3,779
  4. 2015Variational Inference with Normalizing Flowscited by 2,170
  5. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 879
  6. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 602
  7. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 181
  8. 2020Stochastic Normalizing Flowscited by 157
  9. 2023Denoising Diffusion Samplerscited by 149
  10. 2021Annealed Flow Transport Monte Carlocited by 90
  11. 2022Continual Repeated Annealed Flow Transport Monte Carlocited by 66
  12. 2022Score-Based Diffusion meets Annealed Importance Samplingcited by 51
6 more
  1. 2021MCMC Variational Inference via Uncorrected Hamiltonian Annealingcited by 39
  2. 2021Monte Carlo Variational Auto-Encoderscited by 36
  3. 2021Differentiable Annealed Importance Sampling and the Perils of Gradient Noisecited by 36
  4. 2020Marginal likelihood computation for model selection and hypothesis testing: an extensive reviewcited by 33
  5. 2022Langevin Diffusion Variational Inferencecited by 26
  6. 2020Sequential Monte Carlo for Sampling Balanced and Compact Redistricting Planscited by 8

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 4; 2025: 17; 2026: 4.

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  1. 2025Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Expertscited by 96
  2. 2024NETS: A Non-Equilibrium Transport Samplercited by 69
  3. 2025Scalable Equilibrium Sampling with Sequential Boltzmann Generatorscited by 38
  4. 2025LEAPS: A discrete neural sampler via locally equivariant networkscited by 31
  5. 2025No Trick, No Treat: Pursuits and Challenges Towards Simulation-free Training of Neural Samplerscited by 28
  6. 2025MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Controlcited by 21
  7. 2025FEAT: Free energy Estimators with Adaptive Transportcited by 16
  8. 2025Discrete Neural Flow Samplers with Locally Equivariant Transformercited by 13
  9. 2024Stein transport for Bayesian inferencecited by 11
  10. 2024Annealing Flow Generative Models Towards Sampling High-Dimensional and Multi-Modal Distributionscited by 11
  11. 2025Microcanonical Langevin Ensembles: Advancing the Sampling of Bayesian Neural Networkscited by 10
  12. 2025Learning Boltzmann Generators via Constrained Mass Transportcited by 9
13 more
  1. 2025DICE: Discrete inverse continuity equation for learning population dynamicscited by 8
  2. 2024Diffusion-PINN Samplercited by 7
  3. 2025Energy-Weighted Flow Matching: Unlocking Continuous Normalizing Flows for Efficient and Scalable Boltzmann Samplingcited by 7
  4. 2025Neural Flow Samplers with Shortcut Modelscited by 5
  5. 2025Are We Really Learning the Score Function? Reinterpreting Diffusion Models Through Wasserstein Gradient Flow Matchingcited by 5
  6. 2026PolicyFlow: Policy Optimization with Continuous Normalizing Flow in Reinforcement Learningcited by 5
  7. 2025When and how can inexact generative models still sample from the data manifold?cited by 4
  8. 2025DoFlow: Flow-based Generative Models for Interventional and Counterfactual Forecasting on Time Seriescited by 4
  9. 2025Energy-based generator matching: A neural sampler for general state spacecited by 3
  10. 2025Diffusion-Augmented Markov Decision Processes for Maximum Entropy Reinforcement Learningcited by 3
  11. 2026Counterdiabatic Hamiltonian Monte Carlocited by 1
  12. 2026CoreFlow: Low-Rank Matrix Generative Modelscited by 1
  13. 2026Wasserstein Gradient Flows and Forward-Only Diffusion Are Not Enough for Multimodal Samplingcited by 0