mlsanityData to 14 Oct 2026

Discrete Feynman-Kac Correctors

arXiv 2601.10403 ↗First posted 15 Jan 2026cs.LGcited by 11

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Discrete diffusion models have recently emerged as a promising alternative to the autoregressive approach for generating discrete sequences. Sample generation via gradual denoising or demasking processes allows them to capture hierarchical non-sequential interdependencies in the data. These custom processes, however, do not assume a flexible control over the distribution of generated samples. We propose Discrete Feynman-Kac Correctors, a framework that allows for controlling the generated distribution of discrete masked diffusion models at inference time. We derive Sequential Monte Carlo (SMC) algorithms that, given a trained discrete diffusion model, control the temperature of the sampled distribution (i.e. perform annealing), sample from the product of marginals of several diffusion processes (e.g. differently conditioned processes), and sample from the product of the marginal with an external reward function, producing likely samples from the target distribution that also have high reward. Notably, our framework does not require any training of additional models or fine-tuning of the original model. We illustrate the utility of our framework in several applications including: efficient sampling from the annealed Boltzmann distribution of the Ising model, improving the performance of language models for code generation and amortized learning, as well as reward-tilted protein sequence generation.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 47 of its 69 references that are in the map. First posted on arXiv 15 Jan 2026.

Builds on

47 of 69 references.

Closest ancestors · 14

Same direction, newest first

  1. 2025Progressive Inference-Time Annealing of Diffusion Models for Sampling from Boltzmann Densities19 Jun
  2. 2025Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts4 Mar
  3. 2025Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physics12 Feb
  4. 2025Debiasing Guidance for Discrete Diffusion with Sequential Monte Carlo10 Feb
  5. 2025A General Framework for Inference-time Scaling and Steering of Diffusion Models12 Jan
  6. 2024The Superposition of Diffusion Models Using the Ito Density Estimator23 Dec
  7. 2024How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Framework4 Oct
  8. 2024Amortizing intractable inference in diffusion models for vision, language, and control31 May
  9. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization7 Aug
  10. 2022From Denoising Diffusions to Denoising Markov Models7 Nov
  11. 2022Classifier-Free Diffusion Guidance26 Jul
  12. 2022A Continuous Time Framework for Discrete Denoising Models30 May
2 more
  1. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov

Other references · 33

  1. 2020Language Models are Few-Shot Learnerscited by 32,419
  2. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  3. 2021Evaluating Large Language Models Trained on Codecited by 8,320
  4. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,355
  5. 2021Program Synthesis with Large Language Modelscited by 3,637
  6. 2023Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Modelscited by 1,476
  7. 2024RULER: What's the Real Context Size of Your Long-Context Language Models?cited by 1,346
  8. 2023Training Diffusion Models with Reinforcement Learningcited by 982
  9. 2025Large Language Diffusion Modelscited by 912
  10. 2024Simple and Effective Masked Diffusion Language Modelscited by 848
  11. 2023ModelScope Text-to-Video Technical Reportcited by 658
  12. 2024Simplified and Generalized Masked Diffusion for Discrete Datacited by 626
21 more
  1. 2023Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolutioncited by 551
  2. 2022DiGress: Discrete Denoising diffusion for graph generationcited by 520
  3. 2023DPOK: Reinforcement Learning for Fine-tuning Text-to-Image Diffusion Modelscited by 450
  4. 2023The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"cited by 407
  5. 2024Discrete Flow Matchingcited by 317
  6. 2024Long-context LLMs Struggle with Long In-context Learningcited by 286
  7. 2023MathPrompter: Mathematical Reasoning using Large Language Modelscited by 236
  8. 2024Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Controlcited by 233
  9. 2023Protein Design with Guided Discrete Diffusioncited by 157
  10. 2024Unlocking Guidance for Discrete State-Space Diffusion and Flow Modelscited by 129
  11. 2024Self-Improvement in Language Models: The Sharpening Mechanismcited by 104
  12. 2024Diffusion Language Models Are Versatile Protein Learnerscited by 98
  13. 2024Fine-Tuning Discrete Diffusion Models via Reward Optimization with Applications to DNA and Protein Designcited by 79
  14. 2024LLM Processes: Numerical Predictive Distributions Conditioned on Natural Languagecited by 55
  15. 2025GenMol: A Drug Discovery Generalist with Discrete Diffusioncited by 50
  16. 2024PepTune: De Novo Generation of Therapeutic Peptides with Multi-Objective-Guided Discrete Diffusioncited by 37
  17. 2024Steering Masked Discrete Diffusion Models via Discrete Denoising Posterior Predictioncited by 32
  18. 2025LEAPS: A discrete neural sampler via locally equivariant networkscited by 31
  19. 2022Plug & Play Directed Evolution of Proteins with Gradient-based Discrete MCMCcited by 17
  20. 2025Amortized In-Context Bayesian Posterior Estimationcited by 15
  21. 2025Discrete Neural Flow Samplers with Locally Equivariant Transformercited by 13

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 11.

11 papers.

  1. 2026Riemannian MeanFlowcited by 8
  2. 2026Contrastive Distribution Matching for Amortized Sequential Monte Carlo in Discrete Diffusioncited by 5
  3. 2026General Multimodal Protein Design Enables DNA-Encoding of Chemistrycited by 4
  4. 2026SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogatecited by 3
  5. 2026A Continuous-Time Reinforcement Learning Framework for Fine-Tuning Discrete Diffusion Modelscited by 2
  6. 2026VGAS: Variance-Reduced Guidance and Adaptive Selection for Training-Free Reward Alignment in Discrete Diffusioncited by 1
  7. 2026FluxLite: Inference-Time Proposal Control for Discrete Diffusion Modelscited by 1
  8. 2026On the Design Space of Discrete Diffusion Online Adaptation for Molecular Optimizationcited by 0
  9. 2026Twist, Don't Tilt: Trajectory-Exact Constrained Decoding for Masked Diffusion Modelscited by 0
  10. 2026Error-Corrected Inference-Time Scaling for Imperfect Diffusion Modelscited by 0
  11. 2026Risk-Calibrated Proposal Transport for Finite-Particle Diffusion Steeringcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Discrete Diffusion Inference-Time Control with Nested Sequential Monte Carlo
  2. 2026Non-Asymptotic Error Bounds for SMC with Biased Proposals: Application to Conditional Diffusion Sampling
  3. 2026Self-Rewarding Sequential Monte Carlo for Masked Diffusion Language Models
  4. 2025Your Absorbing Discrete Diffusion Secretly Models the Bayesian Posterior
  5. 2026The Diffusion Duality, Chapter II: Psi-Samplers
  6. 2026Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guarantees
  7. 2025Encoder-Decoder Diffusion Language Models for Efficient Training and Inference
  8. 2026From Scores to Gibbs Correctors: Accelerating Uniform-Rate Discrete Diffusion Models