mlsanityData to 14 Oct 2026

Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts

arXiv 2503.02819 ↗First posted 4 Mar 2025cs.LGcited by 96

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling inference-time behavior in a principled manner, e.g. for composing multiple pretrained models. Existing classifier-free guidance methods use a simple heuristic to mix conditional and unconditional scores to approximately sample from conditional distributions. However, such methods do not approximate the intermediate distributions, necessitating additional `corrector' steps. In this work, we provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models. We derive a weighted simulation scheme which we call Feynman-Kac Correctors (FKCs) based on the celebrated Feynman-Kac formula by carefully accounting for terms in the appropriate partial differential equations (PDEs). To simulate these PDEs, we propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality. We empirically demonstrate the utility of our methods by proposing amortized sampling via inference-time temperature annealing, improving multi-objective molecule generation using pretrained models, and improving classifier-free guidance for text-to-image generation. Our code is available at https://github.com/martaskrt/fkc-diffusion.

Key facts. Cited by 96 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 52 of its 84 references that are in the map. First posted on arXiv 4 Mar 2025.

Builds on

52 of 84 references.

Closest ancestors · 16

Same direction, newest first

  1. 2025Debiasing Guidance for Discrete Diffusion with Sequential Monte Carlo10 Feb
  2. 2025Inference-Time Alignment in Diffusion Models with Reward-Guided Generation: Tutorial and Review16 Jan
  3. 2025A General Framework for Inference-time Scaling and Steering of Diffusion Models12 Jan
  4. 2025Test-time Alignment of Diffusion Models without Reward Over-optimization10 Jan
  5. 2024The Superposition of Diffusion Models Using the Ito Density Estimator23 Dec
  6. 2024Diffusion Models as Cartoonists: The Curious Case of High Density Regions2 Nov
  7. 2024Classifier-Free Guidance is a Predictor-Corrector16 Aug
  8. 2024Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decoding15 Aug
  9. 2024Guiding a Diffusion Model with a Bad Version of Itself4 Jun
  10. 2024Target Score Matching13 Feb
  11. 2024Particle Denoising Diffusion Sampler9 Feb
  12. 2023Analyzing and Improving the Training Dynamics of Diffusion Models5 Dec
4 more
  1. 2023Denoising Diffusion Samplers27 Feb
  2. 2023Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC22 Feb
  3. 2022Classifier-Free Diffusion Guidance26 Jul
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov

Other references · 36

  1. 2021Learning Transferable Visual Models From Natural Language Supervisioncited by 33,744
  2. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,355
  3. 2023ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generationcited by 1,045
  4. 2023GenEval: An Object-Focused Framework for Evaluating Text-to-Image Alignmentcited by 972
  5. 2024Simple and Effective Masked Diffusion Language Modelscited by 848
  6. 2022Compositional Visual Generation with Composable Diffusion Modelscited by 624
  7. 2018Pyro: Deep Universal Probabilistic Programmingcited by 380
  8. 2021Therapeutics Data Commons: Machine Learning Datasets and Tasks for Drug Discovery and Developmentcited by 264
  9. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 250
  10. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 232
  11. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 181
  12. 20233D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Predictioncited by 177
24 more
  1. 2015Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measurescited by 139
  2. 2022Flow Annealed Importance Sampling Bootstrapcited by 127
  3. 2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 116
  4. 2023Improved sampling via learned diffusionscited by 104
  5. 2024Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Reviewcited by 98
  6. 2021Annealed Flow Transport Monte Carlocited by 90
  7. 2024Generator Matching: Generative modeling with arbitrary Markov processescited by 86
  8. 2024NETS: A Non-Equilibrium Transport Samplercited by 69
  9. 2023Monte Carlo guided Diffusion for Bayesian linear inverse problemscited by 66
  10. 2019Elements of Sequential Monte Carlocited by 64
  11. 2024Efficient Evolutionary Search Over Chemical Space with Large Language Modelscited by 61
  12. 2025GenMol: A Drug Discovery Generalist with Discrete Diffusioncited by 50
  13. 2024Sequential Controlled Langevin Diffusionscited by 48
  14. 2019Accelerating Langevin Sampling with Birth-deathcited by 45
  15. 2023Learning Interpolations between Boltzmann Densitiescited by 43
  16. 2024Compositional Generative Modeling: A Single Model is Not All You Needcited by 41
  17. 2024Sampling in Unit Time with Kernel Fisher-Rao Flowcited by 27
  18. 2024Liouville Flow Importance Samplercited by 25
  19. 2023Transport meets Variational Inference: Controlled Monte Carlo Diffusionscited by 21
  20. 2024BNEM: A Boltzmann Sampler Based on Bootstrapped Noised Energy Matchingcited by 15
  21. 2024Iterated Energy-based Flow Matching for Sampling from Boltzmann Densitiescited by 13
  22. 2024Neural Sampling from Boltzmann Densities: Fisher-Rao Curves in the Wasserstein Geometrycited by 13
  23. 2024Reprogramming Pretrained Target-Specific Diffusion Models for Dual-Target Drug Designcited by 11
  24. 2024Path-Guided Particle-based Samplingcited by 8

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 29; 2026: 67.

96 papers.

Sort:

By area:

  1. 2025Reasoning with Sampling: Your Base Model is Smarter Than You Thinkcited by 89
  2. 2026Q-learning with Adjoint Matchingcited by 37
  3. 2025Diffusion Tree Sampling: Scalable inference-time alignment of diffusion modelscited by 34
  4. 2026Diamond Maps: Efficient Reward Alignment via Stochastic Flow Mapscited by 29
  5. 2025Progressive Inference-Time Annealing of Diffusion Models for Sampling from Boltzmann Densitiescited by 26
  6. 2025DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Modelscited by 23
  7. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  8. 2025RNE: plug-and-play diffusion inference-time control and energy-based trainingcited by 17
  9. 2025GLASS Flows: Transition Sampling for Alignment of Flow and Diffusion Modelscited by 17
  10. 2025Test-time scaling of diffusions with flow mapscited by 16
  11. 2025Inference-Time Scaling of Discrete Diffusion Models via Importance Weighting and Optimal Proposal Designcited by 14
  12. 2025TR2-D2: Tree Search Guided Trajectory-Aware Fine-Tuning for Discrete Diffusioncited by 14
38 more
  1. 2025Learn to Guide Your Diffusion Modelcited by 14
  2. 2025Progressive Tempering Sampler with Diffusioncited by 13
  3. 2025Flow Matching with Semidiscrete Couplingscited by 13
  4. 2026Enhanced Diffusion Sampling: Efficient Rare Event Sampling and Free Energy Calculation with Diffusion Modelscited by 13
  5. 2025CREPE: Controlling Diffusion with Replica Exchangecited by 11
  6. 2026Discrete Feynman-Kac Correctorscited by 11
  7. 2025Adaptive Diffusion Guidance via Stochastic Optimal Controlcited by 10
  8. 2025Inference-Time Alignment Control for Diffusion Models with Reinforcement Learning Guidancecited by 10
  9. 2026Riemannian MeanFlowcited by 8
  10. 2025Temporal Score Rescaling for Temperature Sampling in Diffusion and Flow Modelscited by 7
  11. 2025Product of Experts for Visual Generationcited by 6
  12. 2025Reinforced sequential Monte Carlo for amortised samplingcited by 6
  13. 2025Conditional Diffusion Models with Classifier-Free Gibbs-like Guidancecited by 5
  14. 2025HollowFlow: Efficient Sample Likelihood Evaluation using Hollow Message Passingcited by 5
  15. 2026Contrastive Distribution Matching for Amortized Sequential Monte Carlo in Discrete Diffusioncited by 5
  16. 2025Controllable protein design with particle-based Feynman-Kac steeringcited by 4
  17. 2025Wavefunction Flows: Efficient Quantum Simulation of Continuous Flow Modelscited by 3
  18. 2025PriorGuide: Test-Time Prior Adaptation for Simulation-Based Inferencecited by 3
  19. 2026Momentum Guidance: Plug-and-Play Guidance for Flow Modelscited by 3
  20. 2026Reject, Resample, Repeat: Understanding Parallel Reasoning in Language Model Inferencecited by 3
  21. 2026Flow Matching for Count Datacited by 3
  22. 2026SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogatecited by 3
  23. 2026Aligning Few-Step Generative Models by Amortizing Sample-based Variational Inferencecited by 3
  24. 2026Fast Organic Crystal Structure Prediction with Unit Cell Flow Matchingcited by 3
  25. 2025Local MAP Sampling for Diffusion Modelscited by 2
  26. 2025Foundations of Diffusion Models in General State Spaces: A Self-Contained Introductioncited by 2
  27. 2026Inference-time optimization for experiment-grounded protein ensemble generationcited by 2
  28. 2026Compression as Adaptation: Implicit Visual Representation with Diffusion Foundation Modelscited by 2
  29. 2026Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measurescited by 2
  30. 2026Stitched Value Model for Diffusion Alignmentcited by 2
  31. 2026Learning Energy-Based Models from Stochastic Interpolants using Spatiotemporal Differencescited by 2
  32. 2026A2D2: Fine-Tuning Any-Length Discrete Diffusion for Adaptive Decodingcited by 2
  33. 2026LatentFlow: A General Framework for Conditioning Stochastic Processescited by 2
  34. 2026Analytic Distribution of Classifier-Free Guidance for Schedule Designcited by 2
  35. 2025Stein Diffusion Guidance: Training-Free Posterior Correction for Sampling Beyond High-Density Regionscited by 1
  36. 2025Ctrl-VI: Controllable Video Synthesis via Variational Inferencecited by 1
  37. 2025ITS3D: Inference-Time Scaling for Text-Guided 3D Diffusion Modelscited by 1
  38. 2026When Are Two Scores Better Than One? Investigating Ensembles of Diffusion Modelscited by 1

50 most cited of 96 All 96 (JSON)

Similar, not cited

Close in wording, no citation either way

  1. 2026Non-Asymptotic Error Bounds for SMC with Biased Proposals: Application to Conditional Diffusion Sampling
  2. 2026Diffusion-Based Posterior Sampling: A Feynman-Kac Analysis of Bias and Stability
  3. 2026Diffusion Path Samplers via Sequential Monte Carlo
  4. 2025Feynman-Kac-Flow: Inference Steering of Conditional Flow Matching to an Energy-Tilted Posterior
  5. 2025Composition and Control with Distilled Energy Diffusion Models and Sequential Monte Carlo
  6. 2025Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physics
  7. 2025From Score Matching to Diffusion: A Fine-Grained Error Analysis in the Gaussian Setting
  8. 2026Metropolis-Adjusted Diffusion Models