mlsanityData to 7 Oct 2026

Sequential Controlled Langevin Diffusions

arXiv 2412.07081 ↗First posted 10 Dec 2024stat.ML cs.AI cs.LGcited by 47

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Cited by 30 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

An effective approach for sampling from unnormalized densities is based on the idea of gradually transporting samples from an easy prior to the complicated target distribution. Two popular methods are (1) Sequential Monte Carlo (SMC), where the transport is performed through successive annealed densities via prescribed Markov chains and resampling steps, and (2) recently developed diffusion-based sampling methods, where a learned dynamical transport is used. Despite the common goal, both approaches have different, often complementary, advantages and drawbacks. The resampling steps in SMC allow focusing on promising regions of the space, often leading to robust performance. While the algorithm enjoys asymptotic guarantees, the lack of flexible, learnable transitions can lead to slow convergence. On the other hand, diffusion-based samplers are learned and can potentially better adapt themselves to the target at hand, yet often suffer from training instabilities. In this work, we present a principled framework for combining SMC with diffusion-based samplers by viewing both methods in continuous time and considering measures on path space. This culminates in the new Sequential Controlled Langevin Diffusion (SCLD) sampling method, which is able to utilize the benefits of both methods and reaches improved performance on multiple benchmark problems, in many cases using only 10% of the training budget of previous diffusion-based samplers.

Key facts. Cited by 47 papers in the map (data through 7 Oct 2026). Builds on 48 of its 84 references that are in the map. First posted on arXiv 10 Dec 2024.

Builds on

48 of 84 references.

References · 48

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  2. 2013Playing Atari with Deep Reinforcement Learningcited by 3,211
  3. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  4. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  5. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 835
  6. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  7. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraintscited by 501
  8. 2022Torsional Diffusion for Molecular Conformer Generationcited by 262
  9. 2024Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Controlcited by 222
  10. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 218
  11. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 216
  12. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 175
36 more
  1. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealingcited by 157
  2. 2020Stochastic Normalizing Flowscited by 156
  3. 2022An optimal control perspective on diffusion-based generative modelingcited by 145
  4. 2023Denoising Diffusion Samplerscited by 144
  5. 2021Solving Schr"odinger Bridges via Maximum Likelihoodcited by 140
  6. 2022Learning GFlowNets from partial episodes for improved convergence and stabilitycited by 129
  7. 2022Flow Annealed Importance Sampling Bootstrapcited by 124
  8. 2023Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systemscited by 118
  9. 2023Improved sampling via learned diffusionscited by 103
  10. 2022Optimal Transport Tools (OTT): A JAX Toolbox for all things Wassersteincited by 96
  11. 2022Action Matching: Learning Stochastic Dynamics from Samplescited by 94
  12. 2021Annealed Flow Transport Monte Carlocited by 90
  13. 2020Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path spacecited by 80
  14. 2024Amortizing intractable inference in diffusion models for vision, language, and controlcited by 70
  15. 2024NETS: A Non-Equilibrium Transport Samplercited by 67
  16. 2022Continual Repeated Annealed Flow Transport Monte Carlocited by 66
  17. 2024Particle Denoising Diffusion Samplercited by 63
  18. 2023Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimizationcited by 57
  19. 2024Beyond ELBOs: A Large-Scale Evaluation of Variational Methods for Samplingcited by 55
  20. 2022Score-Based Diffusion meets Annealed Importance Samplingcited by 51
  21. 2021MCMC Variational Inference via Uncorrected Hamiltonian Annealingcited by 39
  22. 2023Stochastic Optimal Control Matchingcited by 39
  23. 2020An invitation to sequential Monte Carlo samplerscited by 33
  24. 2022Langevin Diffusion Variational Inferencecited by 26
  25. 2024BlackJAX: Composable Bayesian inference in JAXcited by 24
  26. 2021Generalized Normalizing Flows via Markov Chainscited by 23
  27. 2023A framework for conditional diffusion modelling with applications in motif scaffolding for protein designcited by 22
  28. 2024Dynamical Measure Transport and Neural PDE Solvers for Samplingcited by 19
  29. 2023An Empirical Study of the Effectiveness of Using a Replay Buffer on Mode Discovery in GFlowNetscited by 17
  30. 2021Efficient Bayesian Sampling Using Normalizing Flows to Assist Markov Chain Monte Carlo Methodscited by 15
  31. 2019Trust-Region Variational Inference with Gaussian Mixture Modelscited by 14
  32. 2019Schr"odinger Bridge Samplerscited by 14
  33. 2024Neural Sampling from Boltzmann Densities: Fisher-Rao Curves in the Wasserstein Geometrycited by 13
  34. 2024A Taxonomy of Loss Functions for Stochastic Optimal Controlcited by 11
  35. 2024Learned Reference-based Diffusion Sampling for multi-modal distributionscited by 9
  36. 2024Importance Corrected Neural JKO Samplingcited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 33; 2026: 14.

47 papers.

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  1. 2025Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Expertscited by 85
  2. 2025Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matchingcited by 78
  3. 2025DIME:Diffusion-Based Maximum Entropy Reinforcement Learningcited by 52
  4. 2025Scalable Equilibrium Sampling with Sequential Boltzmann Generatorscited by 36
  5. 2025Underdamped Diffusion Bridges with Applications to Samplingcited by 28
  6. 2025Progressive Inference-Time Annealing of Diffusion Models for Sampling from Boltzmann Densitiescited by 26
  7. 2025Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inferencecited by 22
  8. 2025Adjoint Schr"odinger Bridge Samplercited by 20
  9. 2025MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Controlcited by 20
  10. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  11. 2025Outsourced diffusion sampling: Efficient posterior inference in latent spaces of generative modelscited by 16
  12. 2025RNE: plug-and-play diffusion inference-time control and energy-based trainingcited by 16
35 more
  1. 2025Proximal Diffusion Neural Samplercited by 16
  2. 2025Value Gradient Guidance for Flow Matching Alignmentcited by 14
  3. 2025Accelerated Parallel Tempering via Neural Transportscited by 13
  4. 2025Discrete Neural Flow Samplers with Locally Equivariant Transformercited by 13
  5. 2025Progressive Tempering Sampler with Diffusioncited by 13
  6. 2025Inference-Time Scaling of Discrete Diffusion Models via Importance Weighting and Optimal Proposal Designcited by 12
  7. 2025Complexity Analysis of Normalizing Constant Estimation: from Jarzynski Equality to Annealed Importance Sampling and beyondcited by 11
  8. 2025On scalable and efficient training of diffusion samplerscited by 10
  9. 2025Improving the evaluation of samplers on multi-modal targetscited by 9
  10. 2025Non-equilibrium Annealed Adjoint Samplercited by 8
  11. 2025Inverse Problem Sampling in Latent Space Using Sequential Monte Carlocited by 7
  12. 2025Rethinking Losses for Diffusion Bridge Samplerscited by 7
  13. 2026Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matchingcited by 7
  14. 2025Energy-Weighted Flow Matching: Unlocking Continuous Normalizing Flows for Efficient and Scalable Boltzmann Samplingcited by 6
  15. 2025Reinforced sequential Monte Carlo for amortised samplingcited by 5
  16. 2025Generative Modeling with Bayesian Sample Inferencecited by 4
  17. 2025End-To-End Learning of Gaussian Mixture Priors for Diffusion Samplercited by 4
  18. 2026Discrete Adjoint Schr"odinger Bridge Samplercited by 4
  19. 2026Flow Sampling: Learning to Sample from Unnormalized Densities via Denoising Conditional Processescited by 4
  20. 2026Sample-efficient evidence estimation of score based priors for model selectioncited by 3
  21. 2025Importance Weighted Score Matching for Diffusion Samplers with Enhanced Mode Coveragecited by 2
  22. 2026Diffusion Path Samplers via Sequential Monte Carlocited by 2
  23. 2026Discrete diffusion samplers and bridges: Off-policy algorithms and applications in latent spacescited by 2
  24. 2026S3: Stratified Scaling Search for Test-Time in Diffusion Language Modelscited by 2
  25. 2026Constrained Diffusion Models with Primal-Dual Inferencecited by 2
  26. 2025Sampling by averaging: A multiscale approach to score estimationcited by 1
  27. 2025One-Step Diffusion Samplers via Self-Distillation and Deterministic Flowcited by 1
  28. 2026Analytic Bridge Diffusions for Controlled Path Generationcited by 1
  29. 2026Exact Global MCMC with Denoising Diffusioncited by 1
  30. 2025Single-Step Consistent Diffusion Samplerscited by 0
  31. 2025Value Gradient Sampler: Learning Invariant Value Functions for Equivariant Diffusion Samplingcited by 0
  32. 2026FES-FM: Free Energy Surface Sampling via Reduced Flow Matchingcited by 0
  33. 2026Tensor Train Diffusion: Leveraging Low-Rank Structures for High-Dimensional Score-Based Samplingcited by 0
  34. 2026Mode Collapse Is Cheap to Detect: A Ground-Truth-Free Pre-Flight Check for Neural Samplerscited by 0
  35. 2026Neural Transport Nested Samplingcited by 0