mlsanityData to 14 Oct 2026

Inference-Time Scaling of Discrete Diffusion Models via Importance Weighting and Optimal Proposal Design

arXiv 2505.22524 ↗First posted 28 May 2025cs.LGcited by 14

On the map: LLM reasoning → Diffusion reasoning and test-time scaling

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Abstract (arXiv)

Discrete diffusion models have become highly effective across various domains. However, real-world applications often require the generative process to adhere to certain constraints. To this end, we propose a Sequential Monte Carlo (SMC) framework that enables scalable inference-time control of discrete diffusion models through principled importance weighting and optimal proposal construction. Specifically, our approach derives tractable importance weights for a range of intermediate targets and characterises the optimal proposal, for which we develop two practical approximations: a first-order gradient-based approximation and an amortised proposal trained to minimise the log-variance of the importance weights. Empirical results across synthetic tasks, language modelling, biology design, and text-to-image generation demonstrate that our framework enhances controllability and sample quality, highlighting the effectiveness of SMC as a versatile recipe for scaling discrete diffusion models at inference time.

Key facts. Cited by 14 papers in the map (data through 14 Oct 2026). Placed in Diffusion reasoning and test-time scaling, one of 17 directions in LLM reasoning. Builds on 47 of its 102 references that are in the map. First posted on arXiv 28 May 2025.

Builds on

47 of 102 references.

Closest ancestors · 3

Same direction, newest first

  1. 2025d1: Scaling Reasoning in Diffusion Large Language Models via Reinforcement Learning16 Apr
  2. 2025Remasking Discrete Diffusion Models with Inference-Time Scaling1 Mar
  3. 2025A General Framework for Inference-time Scaling and Steering of Diffusion Models12 Jan

Other references · 44

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 9,379
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  4. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,330
  5. 2022Classifier-Free Diffusion Guidancecited by 5,847
  6. 2013Auto-Encoding Variational Bayescited by 4,053
  7. 2016Categorical Reparameterization with Gumbel-Softmaxcited by 2,739
  8. 2017Decoupled Weight Decay Regularizationcited by 1,831
  9. 2023Training Diffusion Models with Reinforcement Learningcited by 982
  10. 2025Large Language Diffusion Modelscited by 912
  11. 2023Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesiscited by 890
  12. 2023Discrete Diffusion Modeling by Estimating the Ratios of the Data Distributioncited by 745
32 more
  1. 2022DiGress: Discrete Denoising diffusion for graph generationcited by 520
  2. 2024Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Designcited by 305
  3. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problemcited by 236
  4. 2022SSD-LM: Semi-autoregressive Simplex-based Diffusion Language Model for Text Generation and Modular Controlcited by 194
  5. 2022Score-based Continuous-time Discrete Diffusion Modelscited by 169
  6. 2024Simple Guidance Mechanisms for Discrete Diffusion Modelscited by 155
  7. 2024Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decodingcited by 136
  8. 2024Unlocking Guidance for Discrete State-Space Diffusion and Flow Modelscited by 129
  9. 2023Improved sampling via learned diffusionscited by 104
  10. 2025Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Expertscited by 96
  11. 2025Test-time Alignment of Diffusion Models without Reward Over-optimizationcited by 93
  12. 2024Probabilistic Inference in Language Models via Twisted Sequential Monte Carlocited by 90
  13. 2025Inference-Time Alignment in Diffusion Models with Reward-Guided Generation: Tutorial and Reviewcited by 88
  14. 2024Fine-Tuning Discrete Diffusion Models via Reward Optimization with Applications to DNA and Protein Designcited by 79
  15. 2023Monte Carlo guided Diffusion for Bayesian linear inverse problemscited by 66
  16. 2024Meissonic: Revitalizing Masked Generative Transformers for Efficient High-Resolution Text-to-Image Synthesiscited by 56
  17. 2024Feedback Efficient Online Fine-Tuning of Diffusion Modelscited by 53
  18. 2024Sequential Controlled Langevin Diffusionscited by 48
  19. 2025Fine-Tuning Discrete Diffusion Models with Policy Gradient Methodscited by 38
  20. 2024Steering Masked Discrete Diffusion Models via Discrete Denoising Posterior Predictioncited by 32
  21. 2024Efficient Diversity-Preserving Diffusion Alignment via Gradient-Informed GFlowNetscited by 32
  22. 2025Debiasing Guidance for Discrete Diffusion with Sequential Monte Carlocited by 31
  23. 2025LEAPS: A discrete neural sampler via locally equivariant networkscited by 31
  24. 2025Test-Time Scaling of Diffusion Models via Noise Trajectory Searchcited by 30
  25. 2025Reward-Guided Iterative Refinement in Diffusion Models at Test-Time with Applications to Protein and DNA Designcited by 25
  26. 2025Target Concrete Score Matching: A Holistic Framework for Discrete Diffusioncited by 25
  27. 2024Step-by-Step Reasoning for Math Problems via Twisted Sequential Monte Carlocited by 22
  28. 2025Rollout Roulette: A Probabilistic Inference Approach to Inference-Time Scaling of LLMs using Particle-Based Monte Carlo Methodscited by 20
  29. 2025Split Gibbs Discrete Diffusion Posterior Samplingcited by 18
  30. 2025Discrete Neural Flow Samplers with Locally Equivariant Transformercited by 13
  31. 2024Plug-and-Play Controllable Generation for Discrete Masked Modelscited by 11
  32. 2025Iterative Importance Fine-tuning of Diffusion Modelscited by 6

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 13.

14 papers.

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  1. 2026Contrastive Distribution Matching for Amortized Sequential Monte Carlo in Discrete Diffusioncited by 5
  2. 2026Entropy Aware Reward Guidance for Diffusion Language Model Alignmentcited by 3
  3. 2026SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogatecited by 3
  4. 2026Plug-and-Play Guidance for Discrete Diffusion Models via Gradient-Informed Logit Correctioncited by 3
  5. 2025Tree Reward-Aligned Search for TReASURe in Masked Diffusion Language Modelscited by 2
  6. 2026Diffusion Alignment Beyond KL: Variance Minimisation as Effective Policy Optimisercited by 1
  7. 2026VGB for Masked Diffusion Model: Efficient Test-time Scaling for Reward Satisfaction and Sample Editingcited by 1
  8. 2026Discrete Diffusion Inference-Time Control with Nested Sequential Monte Carlocited by 1
  9. 2026VGAS: Variance-Reduced Guidance and Adaptive Selection for Training-Free Reward Alignment in Discrete Diffusioncited by 1
  10. 2026FluxLite: Inference-Time Proposal Control for Discrete Diffusion Modelscited by 1
  11. 2026Parallel Tempering for Diffusion-Based Combinatorial Optimizationcited by 0
  12. 2026Specificity-Aware Diffusion Steering via Variance-Reduced Sequential Monte Carlocited by 0
2 more
  1. 2026Learn Feasibility Once, Optimize All Objectives: Derivative-Free Diffusion Models for Chance-Constrained Programmingcited by 0
  2. 2026Risk-Calibrated Proposal Transport for Finite-Particle Diffusion Steeringcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Navigating the Exploration-Exploitation Tradeoff in Inference-Time Scaling of Diffusion Models
  2. 2026Inference-Time Scaling in Diffusion Models through Iterative Partial Refinement
  3. 2026Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measures
  4. 2025Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithms
  5. 2025Inference-time Scaling of Diffusion Models through Classical Search
  6. 2025Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physics
  7. 2025Inference-Time Scaling for Diffusion Models beyond Scaling Denoising Steps
  8. 2026Self-Rewarding Sequential Monte Carlo for Masked Diffusion Language Models