mlsanityData to 7 Oct 2026

Discrete Diffusion Inference-Time Control with Nested Sequential Monte Carlo

arXiv 2608.20123 ↗First posted 20 Aug 2026stat.ML cs.LGcited by 1

On the map: Diffusion models → Discrete and text diffusion

Abstract (arXiv)

We study inference-time control for text generation in discrete diffusion language models, where the goal is to steer sampling toward sequence-level rewards without retraining. Prior work in this domain has focused on particle-based methods such as best-of-n sampling and bootstrap sequential Monte Carlo, which may suffer from overoptimism and weight degeneracy, respectively. We address these limitations using nested sequential Monte Carlo methods. We formulate nested SMC (NSMC) and fully-adapted nested SMC (FA-NSMC) for Feynman--Kac steering, identifying and correcting errors in prior formulations that lead to biased final estimates. We evaluate these methods on toxicity and fluency steering tasks, showing that NSMC and FA-NSMC consistently outperform best-of-n and bootstrap SMC.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Placed in Discrete and text diffusion, one of 14 directions in Diffusion models. Builds on 27 of its 42 references that are in the map. First posted on arXiv 20 Aug 2026.

Builds on

27 of 42 references.

Closest ancestors · 5

Same direction, newest first

  1. 2025Dream 7B: Diffusion Large Language Models21 Aug
  2. 2025Large Language Diffusion Models14 Feb
  3. 2024Simple and Effective Masked Diffusion Language Models11 Jun
  4. 2024Simplified and Generalized Masked Diffusion for Discrete Data6 Jun
  5. 2022SSD-LM: Semi-autoregressive Simplex-based Diffusion Language Model for Text Generation and Modular Control31 Oct

Other references · 22

  1. 2022Training language models to follow instructions with human feedbackcited by 15,712
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  3. 2023Judging LLM-as-a-Judge with MT-Bench and Chatbot Arenacited by 8,393
  4. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  5. 2021TruthfulQA: Measuring How Models Mimic Human Falsehoodscited by 2,919
  6. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  7. 2024HarmBench: A Standardized Evaluation Framework for Automated Red Teaming and Robust Refusalcited by 1,330
  8. 2021BOLD: Dataset and Metrics for Measuring Biases in Open-Ended Language Generationcited by 410
  9. 2023Understanding the Effects of RLHF on LLM Generalisation and Diversitycited by 386
  10. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problemcited by 229
  11. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 218
  12. 2025A General Framework for Inference-time Scaling and Steering of Diffusion Modelscited by 201
10 more
  1. 2022"I'm sorry to hear that": Finding New Biases in Language Models with a Holistic Descriptor Datasetcited by 160
  2. 2023Protein Design with Guided Discrete Diffusioncited by 154
  3. 2020Evaluating the Evaluation of Diversity in Natural Language Generationcited by 127
  4. 2024Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decodingcited by 127
  5. 2025Inference-Time Alignment in Diffusion Models with Reward-Guided Generation: Tutorial and Reviewcited by 82
  6. 2019Elements of Sequential Monte Carlocited by 60
  7. 2015Nested Sequential Monte Carlo Methodscited by 19
  8. 2025Inference-Time Scaling of Discrete Diffusion Models via Importance Weighting and Optimal Proposal Designcited by 12
  9. 2024Diffusion Rejection Samplingcited by 11
  10. 2016High-dimensional Filtering using Nested Sequential Monte Carlocited by 8

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026VGAS: Variance-Reduced Guidance and Adaptive Selection for Training-Free Reward Alignment in Discrete Diffusioncited by 0

Similar, not cited

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  1. 2026Discrete Feynman-Kac Correctors
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  3. 2026FluxLite: Inference-Time Proposal Control for Discrete Diffusion Models
  4. 2026Reject, Resample, Repeat: Understanding Parallel Reasoning in Language Model Inference
  5. 2025Navigating the Exploration-Exploitation Tradeoff in Inference-Time Scaling of Diffusion Models
  6. 2025Inference-Time Scaling of Diffusion Language Models via Trajectory Refinement
  7. 2025Diffusion Language Model Inference with Monte Carlo Tree Search
  8. 2025Debiasing Guidance for Discrete Diffusion with Sequential Monte Carlo