mlsanityData to 7 Oct 2026

Dirichlet Flow Matching with Applications to DNA Sequence Design

arXiv 2402.05841 ↗First posted 8 Feb 2024q-bio.BM cs.LGcited by 110

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

Discrete diffusion or flow models could enable faster and more controllable sequence generation than autoregressive models. We show that na"ive linear flow matching on the simplex is insufficient toward this goal since it suffers from discontinuities in the training target and further pathologies. To overcome this, we develop Dirichlet flow matching on the simplex based on mixtures of Dirichlet distributions as probability paths. In this framework, we derive a connection between the mixtures' scores and the flow's vector field that allows for classifier and classifier-free guidance. Further, we provide distilled Dirichlet flow matching, which enables one-step sequence generation with minimal performance hits, resulting in O(L) speedups compared to autoregressive models. On complex DNA sequence generation tasks, we demonstrate superior performance compared to all baselines in distributional metrics and in achieving desired design targets for generated sequences. Finally, we show that our classifier-free guidance approach improves unconditional generation and is effective for generating DNA that satisfies design targets. Code is available at https://github.com/HannesStark/dirichlet-flow-matching.

Key facts. Cited by 110 papers in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 33 of its 47 references that are in the map. First posted on arXiv 8 Feb 2024.

Builds on

33 of 47 references.

Closest ancestors · 11

Same direction, newest first

  1. 2023Guided Flows for Generative Modeling and Decision Making22 Nov
  2. 2023Latent Diffusion Model for DNA Sequence Generation9 Oct
  3. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generation3 Oct
  4. 2023Flow Matching in Latent Space17 Jul
  5. 2023Dirichlet Diffusion Score Model for Biological Sequence Generation18 May
  6. 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplings28 Apr
  7. 2023Flow Matching on General Geometries7 Feb
  8. 2023Improving and generalizing flow-based generative models with minibatch optimal transport1 Feb
  9. 2022Flow Matching for Generative Modeling6 Oct
  10. 2022DiGress: Discrete Denoising diffusion for graph generation29 Sep
  11. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 22

  1. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  3. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  4. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  5. 2022Classifier-Free Diffusion Guidancecited by 5,717
  6. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  7. 2023Consistency Modelscited by 1,778
  8. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  9. 2023One-step Diffusion with Distribution Matching Distillationcited by 978
  10. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  11. 2022A Continuous Time Framework for Discrete Denoising Modelscited by 437
  12. 2022Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioningcited by 362
10 more
  1. 2021Autoregressive Diffusion Modelscited by 208
  2. 2022Continuous diffusion for categorical datacited by 202
  3. 2018Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discoverycited by 191
  4. 2022SSD-LM: Semi-autoregressive Simplex-based Diffusion Language Model for Text Generation and Modular Controlcited by 191
  5. 2023Restart Sampling for Improving Generative Processescited by 81
  6. 2013Projection onto the probability simplex: An efficient algorithm with a simple proof, and an applicationcited by 65
  7. 2022Categorical SDEs with Simplex Diffusioncited by 42
  8. 2023Protein Discovery with Discrete Walk-Jump Samplingcited by 38
  9. 2023RetroBridge: Modeling Retrosynthesis with Markov Bridgescited by 35
  10. 2023Diffusion on the Probability Simplexcited by 14

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 29; 2025: 45; 2026: 36.

110 papers.

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  1. 2024Discrete Flow Matchingcited by 301
  2. 2024Simple Guidance Mechanisms for Discrete Diffusion Modelscited by 148
  3. 2024Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decodingcited by 127
  4. 2024Unlocking Guidance for Discrete State-Space Diffusion and Flow Modelscited by 124
  5. 2024Consistency Flow Matching: Defining Straight Flows with Velocity Consistencycited by 101
  6. 2024Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Reviewcited by 92
  7. 2024PnP-Flow: Plug-and-Play Image Restoration with Flow Matchingcited by 92
  8. 2024Variational Flow Matching for Graph Generationcited by 78
  9. 2024Fine-Tuning Discrete Diffusion Models via Reward Optimization with Applications to DNA and Protein Designcited by 72
  10. 2024Fisher Flow Matching for Generative Modeling over Discrete Datacited by 68
  11. 2024Mixed Continuous and Categorical Flow Matching for 3D De Novo Molecule Generationcited by 53
  12. 2024Generative Modeling of Molecular Dynamics Trajectoriescited by 48
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. 2024Categorical Flow Matching on Statistical Manifoldscited by 43
  4. 2024Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexitycited by 42
  5. 2024SemlaFlow -- Efficient 3D Molecular Generation with Latent Attention and Equivariant Flow Matchingcited by 40
  6. 2026Categorical Flow Mapscited by 37
  7. 2025Fine-Tuning Discrete Diffusion Models with Policy Gradient Methodscited by 36
  8. 2024PepTune: De Novo Generation of Therapeutic Peptides with Multi-Objective-Guided Discrete Diffusioncited by 35
  9. 2025Time Is a Feature: Exploiting Temporal Dynamics in Diffusion Language Modelscited by 33
  10. 2025Continuously Augmented Discrete Diffusion model for Categorical Generative Modelingcited by 32
  11. 2025Continuous Diffusion Model for Language Modelingcited by 29
  12. 2024Wasserstein Flow Matching: Generative modeling over families of distributionscited by 27
  13. 2025WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetrycited by 25
  14. 2024Bridging Model-Based Optimization and Generative Modeling via Conservative Fine-Tuning of Diffusion Modelscited by 24
  15. 2025Training-Free Guidance Beyond Differentiability: Scalable Path Steering with Tree Search in Diffusion and Flow Modelscited by 23
  16. 2026Discrete Flow Mapscited by 23
  17. 2025Reward-Guided Iterative Refinement in Diffusion Models at Test-Time with Applications to Protein and DNA Designcited by 21
  18. 2025α-Flow: A Unified Framework for Continuous-State Discrete Flow Matching Modelscited by 17
  19. 2025CtrlDiff: Boosting Large Diffusion Language Models with Dynamic Block Prediction and Controllable Generationcited by 17
  20. 2025Exponential Family Variational Flow Matching for Tabular Data Generationcited by 15
  21. 2025Offline Model-Based Optimization: Comprehensive Reviewcited by 14
  22. 2025Flow Matching Meets Biology and Life Science: A Surveycited by 14
  23. 2025Multi-Objective-Guided Discrete Flow Matching for Controllable Biological Sequence Designcited by 13
  24. 2025TR2-D2: Tree Search Guided Trajectory-Aware Fine-Tuning for Discrete Diffusioncited by 13
  25. 2024Exploring Discrete Flow Matching for 3D De Novo Molecule Generationcited by 11
  26. 2025Gumbel-Softmax Flow Matching with Straight-Through Guidance for Controllable Biological Sequence Generationcited by 11
  27. 2024HELM: Hierarchical Encoding for mRNA Language Modelingcited by 9
  28. 2025What Exactly Does Guidance Do in Masked Discrete Diffusion Modelscited by 9
  29. 2025Controlled Generation with Equivariant Variational Flow Matchingcited by 9
  30. 2026Improving Flow Matching by Aligning Flow Divergencecited by 9
  31. 2024EventFlow: Forecasting Temporal Point Processes with Flow Matchingcited by 8
  32. 2025Steering Generative Models with Experimental Data for Protein Fitness Optimizationcited by 7
  33. 2025Bures-Wasserstein Flow Matching for Graph Generationcited by 7
  34. 2024Generative Assignment Flows for Representing and Learning Joint Distributions of Discrete Datacited by 6
  35. 2025Compositional Flows for 3D Molecule and Synthesis Pathway Co-designcited by 6
  36. 2025Hierarchical Rectified Flow Matching with Mini-Batch Couplingscited by 6
  37. 2026Scaling Categorical Flow Mapscited by 6
  38. 2026Hacking Generative Perplexity: Why Unconditional Text Evaluation Needs Distributional Metricscited by 6

50 most cited of 110 All 110 (JSON)

Similar, not cited

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  1. 2024Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design
  2. 2024DiscDiff: Latent Diffusion Model for DNA Sequence Generation
  3. 2025Branching Flows: Discrete, Continuous, and Manifold Flow Matching with Splits and Deletions
  4. 2024Flow Matching with General Discrete Paths: A Kinetic-Optimal Perspective
  5. 2025Discrete Diffusion Trajectory Alignment via Stepwise Decomposition
  6. 2024Meta Flow Matching: Integrating Vector Fields on the Wasserstein Manifold
  7. 2026EvoFlows: Evolutionary Edit-Based Flow-Matching for Protein Engineering
  8. 2024A survey of probabilistic generative frameworks for molecular simulations