mlsanityData to 14 Oct 2026

Unlocking Guidance for Discrete State-Space Diffusion and Flow Models

arXiv 2406.01572 ↗First posted 3 Jun 2024cs.LGcited by 129

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Cited by 93 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Generative models on discrete state-spaces have a wide range of potential applications, particularly in the domain of natural sciences. In continuous state-spaces, controllable and flexible generation of samples with desired properties has been realized using guidance on diffusion and flow models. However, these guidance approaches are not readily amenable to discrete state-space models. Consequently, we introduce a general and principled method for applying guidance on such models. Our method depends on leveraging continuous-time Markov processes on discrete state-spaces, which unlocks computational tractability for sampling from a desired guided distribution. We demonstrate the utility of our approach, Discrete Guidance, on a range of applications including guided generation of small-molecules, DNA sequences and protein sequences.

Key facts. Cited by 129 papers in the map (data through 14 Oct 2026). Builds on 56 of its 101 references that are in the map. First posted on arXiv 3 Jun 2024.

Builds on

56 of 101 references.

References · 56

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  3. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  4. 2017Proximal Policy Optimization Algorithmscited by 15,215
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  6. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  7. 2023Direct Preference Optimization: Your Language Model is Secretly a Reward Modelcited by 8,065
  8. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  9. 2022Classifier-Free Diffusion Guidancecited by 5,847
  10. 2022Flow Matching for Generative Modelingcited by 5,702
  11. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,700
  12. 2016Improved Techniques for Training GANscited by 2,970
38 more
  1. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,719
  2. 2022Diffusion-LM Improves Controllable Text Generationcited by 1,027
  3. 2022Building Normalizing Flows with Stochastic Interpolantscited by 995
  4. 2019Plug and Play Language Models: A Simple Approach to Controlled Text Generationcited by 799
  5. 2016Automatic chemical design using a data-driven continuous representation of moleculescited by 765
  6. 2024SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformerscited by 737
  7. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 677
  8. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 574
  9. 2022DiGress: Discrete Denoising diffusion for graph generationcited by 520
  10. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 516
  11. 2022A Continuous Time Framework for Discrete Denoising Modelscited by 451
  12. 2022DiffuSeq: Sequence to Sequence Text Generation with Diffusion Modelscited by 450
  13. 2021FUDGE: Controlled Text Generation With Future Discriminatorscited by 376
  14. 2022Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioningcited by 373
  15. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 313
  16. 2024Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Designcited by 305
  17. 2023Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMCcited by 220
  18. 2022Continuous diffusion for categorical datacited by 214
  19. 2021Autoregressive Diffusion Modelscited by 210
  20. 2022SSD-LM: Semi-autoregressive Simplex-based Diffusion Language Model for Text Generation and Modular Controlcited by 194
  21. 2022Score-based Continuous-time Discrete Diffusion Modelscited by 169
  22. 2023Flow Matching in Latent Spacecited by 160
  23. 2023Protein Design with Guided Discrete Diffusioncited by 157
  24. 2023Likelihood-Based Diffusion Language Modelscited by 151
  25. 2022Concrete Score Matching: Generalized Score Matching for Discrete Datacited by 148
  26. 2022Self-conditioned Embedding Diffusion for Text Generationcited by 117
  27. 2024Dirichlet Flow Matching with Applications to DNA Sequence Designcited by 115
  28. 2023Guided Flows for Generative Modeling and Decision Makingcited by 101
  29. 2024Diffusion Language Models Are Versatile Protein Learnerscited by 98
  30. 2021Oops I Took A Gradient: Scalable Sampling for Discrete Distributionscited by 92
  31. 2023Dirichlet Diffusion Score Model for Biological Sequence Generationcited by 75
  32. 2019Neural Empirical Bayescited by 46
  33. 2022A Langevin-like Sampler for Discrete Distributionscited by 44
  34. 2022Categorical SDEs with Simplex Diffusioncited by 42
  35. 2023Protein Discovery with Discrete Walk-Jump Samplingcited by 38
  36. 2022State-specific protein-ligand complex structure prediction with a multi-scale deep generative modelcited by 35
  37. 2023Blackout Diffusion: Generative Diffusion Models in Discrete-State Spacescited by 30
  38. 2023Sparse Training of Discrete Diffusion Models for Graph Generationcited by 27

50 most cited of 56 All 56 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 14; 2025: 63; 2026: 52.

129 papers.

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  1. 2024Simplified and Generalized Masked Diffusion for Discrete Datacited by 626
  2. 2025Block Diffusion: Interpolating Between Autoregressive and Diffusion Language Modelscited by 409
  3. 2025Remasking Discrete Diffusion Models with Inference-Time Scalingcited by 189
  4. 2024Simple Guidance Mechanisms for Discrete Diffusion Modelscited by 155
  5. 2024Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decodingcited by 136
  6. 2025The Diffusion Dualitycited by 135
  7. 2025Inference-Time Alignment in Diffusion Models with Reward-Guided Generation: Tutorial and Reviewcited by 88
  8. 2024Fine-Tuning Discrete Diffusion Models via Reward Optimization with Applications to DNA and Protein Designcited by 79
  9. 2025Discrete Diffusion in Large Language and Multimodal Models: A Surveycited by 61
  10. 2024Flow Matching with General Discrete Paths: A Kinetic-Optimal Perspectivecited by 57
  11. 2025Edit Flows: Flow Matching with Edit Operationscited by 55
  12. 2025GenMol: A Drug Discovery Generalist with Discrete Diffusioncited by 50
38 more
  1. 2024How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Frameworkcited by 48
  2. 2025Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithmscited by 47
  3. 2025Fine-Tuning Discrete Diffusion Models with Policy Gradient Methodscited by 38
  4. 2024PepTune: De Novo Generation of Therapeutic Peptides with Multi-Objective-Guided Discrete Diffusioncited by 37
  5. 2025Dynamic Search for Inference-Time Alignment in Diffusion Modelscited by 37
  6. 2025Esoteric Language Models: A Family of Any-Order Diffusion LLMscited by 34
  7. 2025Continuously Augmented Discrete Diffusion model for Categorical Generative Modelingcited by 34
  8. 2024Steering Masked Discrete Diffusion Models via Discrete Denoising Posterior Predictioncited by 32
  9. 2025Debiasing Guidance for Discrete Diffusion with Sequential Monte Carlocited by 31
  10. 2025d2: Improving Reasoning in Diffusion Language Models via Trajectory Likelihood Estimationcited by 27
  11. 2025Reward-Guided Iterative Refinement in Diffusion Models at Test-Time with Applications to Protein and DNA Designcited by 25
  12. 2025Target Concrete Score Matching: A Holistic Framework for Discrete Diffusioncited by 25
  13. 2025Training-Free Guidance Beyond Differentiability: Scalable Path Steering with Tree Search in Diffusion and Flow Modelscited by 24
  14. 2026Language Modeling with Hyperspherical Flowscited by 22
  15. 2025Diffuse Everything: Multimodal Diffusion Models on Arbitrary State Spacescited by 21
  16. 2025MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Controlcited by 21
  17. 2025Beyond Masked and Unmasked: Discrete Diffusion Models via Partial Maskingcited by 20
  18. 2025Discrete Diffusion Models: Novel Analysis and New Sampler Guaranteescited by 20
  19. 2025Enhancing Reasoning for Diffusion LLMs via Distribution Matching Policy Optimizationcited by 20
  20. 2025Split Gibbs Discrete Diffusion Posterior Samplingcited by 18
  21. 2025CtrlDiff: Boosting Large Diffusion Language Models with Dynamic Block Prediction and Controllable Generationcited by 17
  22. 2025Multi-Objective-Guided Discrete Flow Matching for Controllable Biological Sequence Designcited by 15
  23. 2025Why Masking Diffusion Works: Condition on the Jump Schedule for Improved Discrete Diffusioncited by 15
  24. 2025Inference-Time Scaling of Discrete Diffusion Models via Importance Weighting and Optimal Proposal Designcited by 14
  25. 2025TR2-D2: Tree Search Guided Trajectory-Aware Fine-Tuning for Discrete Diffusioncited by 14
  26. 2025Preference-Based Alignment of Discrete Diffusion Modelscited by 13
  27. 2025Learning Diffusion Models with Flexible Representation Guidancecited by 13
  28. 2025ReAlign: Text-to-Motion Generation via Step-Aware Reward-Guided Alignmentcited by 13
  29. 2025Fast and Accurate Causal Parallel Decoding using Jacobi Forcingcited by 13
  30. 2025Discrete Diffusion Trajectory Alignment via Stepwise Decompositioncited by 12
  31. 2026The Diffusion Duality, Chapter II: Psi-Samplerscited by 12
  32. 2024Plug-and-Play Controllable Generation for Discrete Masked Modelscited by 11
  33. 2025Gumbel-Softmax Flow Matching with Straight-Through Guidance for Controllable Biological Sequence Generationcited by 11
  34. 2025Iterative Distillation for Reward-Guided Fine-Tuning of Diffusion Models in Biomolecular Designcited by 11
  35. 2025Improving Classifier-Free Guidance in Masked Diffusion: Low-Dim Theoretical Insights with High-Dim Impactcited by 11
  36. 2026Discrete Feynman-Kac Correctorscited by 11
  37. 2025What Exactly Does Guidance Do in Masked Discrete Diffusion Modelscited by 9
  38. 2026Sharp Convergence Rates for Masked Diffusion Modelscited by 9

50 most cited of 129 All 129 (JSON)

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  1. 2024Training-Free Guidance for Discrete Diffusion Models for Molecular Generation
  2. 2024Context-Guided Diffusion for Out-of-Distribution Molecular and Protein Design
  3. 2025Branching Flows: Discrete, Continuous, and Manifold Flow Matching with Splits and Deletions
  4. 2025Bit-Level Discrete Diffusion with Markov Probabilistic Models: An Improved Framework with Sharp Convergence Bounds under Minimal Assumptions
  5. 2023Particle Guidance: non-I.I.D. Diverse Sampling with Diffusion Models
  6. 2024Discrete-state Continuous-time Diffusion for Graph Generation
  7. 2026Why Gaussian Diffusion Models Fail on Discrete Data and How to Prevent It?
  8. 2026Acceleration of Diffusion Language Model through Discrete Average Generator