mlsanityData to 7 Oct 2026

Categorical Flow Maps

arXiv 2602.12233 ↗First posted 12 Feb 2026cs.LGcited by 37

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

Abstract (arXiv)

We introduce Categorical Flow Maps, a flow-matching method for accelerated few-step generation of categorical data via self-distillation. Building on recent variational formulations of flow matching and the broader trend towards accelerated inference in diffusion and flow-based models, we define a flow map towards the simplex that transports probability mass toward a predicted endpoint, yielding a parametrisation that naturally constrains model predictions. Since our trajectories are continuous rather than discrete, Categorical Flow Maps can be trained with existing distillation techniques, as well as a new objective based on endpoint consistency. This continuous formulation also automatically unlocks test-time inference: we can directly reuse existing guidance and reweighting techniques in the categorical setting to steer sampling toward downstream objectives. Empirically, we achieve state-of-the-art few-step results on images, molecular graphs, and text, with strong performance even in single-step generation.

Key facts. Cited by 37 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 61 of its 72 references that are in the map. First posted on arXiv 12 Feb 2026.

Builds on

61 of 72 references.

Closest ancestors · 22

Same direction, newest first

  1. 2025Terminal Velocity Matching24 Nov
  2. 2025Generalised Flow Maps for Few-Step Generative Modelling on Riemannian Manifolds24 Oct
  3. 2025Purrception: Variational Flow Matching for Vector-Quantized Image Generation1 Oct
  4. 2025Controlled Generation with Equivariant Variational Flow Matching23 Jun
  5. 2025Align Your Flow: Scaling Continuous-Time Flow Map Distillation17 Jun
  6. 2025Exponential Family Variational Flow Matching for Tabular Data Generation6 Jun
  7. 2025How to build a consistency model: Learning flow maps via self-distillation24 May
  8. 2024DeFoG: Discrete Flow Matching for Graph Generation5 Oct
  9. 2024Discrete Flow Matching22 Jul
  10. 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency models11 Jun
  11. 2024Cometh: A continuous-time discrete-state graph diffusion model10 Jun
  12. 2024Variational Flow Matching for Graph Generation7 Jun
10 more
  1. 2024Categorical Flow Matching on Statistical Manifolds26 May
  2. 2024Fisher Flow Matching for Generative Modeling over Discrete Data23 May
  3. 2024Discrete-state Continuous-time Diffusion for Graph Generation19 May
  4. 2024Mixed Continuous and Categorical Flow Matching for 3D De Novo Molecule Generation30 Apr
  5. 2024Dirichlet Flow Matching with Applications to DNA Sequence Design8 Feb
  6. 2024Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design7 Feb
  7. 2022Flow Matching for Generative Modeling6 Oct
  8. 2022DiGress: Discrete Denoising diffusion for graph generation29 Sep
  9. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep
  10. 2022Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations5 Feb

Other references · 39

  1. 2022Scalable Diffusion Models with Transformerscited by 5,931
  2. 2016Layer Normalizationcited by 5,579
  3. 2017FiLM: Visual Reasoning with a General Conditioning Layercited by 2,286
  4. 2023Consistency Modelscited by 1,778
  5. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  6. 2017Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semanticscited by 1,345
  7. 2017MoleculeNet: A Benchmark for Molecular Machine Learningcited by 1,037
  8. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  9. 2025Large Language Diffusion Modelscited by 872
  10. 2024Simple and Effective Masked Diffusion Language Modelscited by 800
  11. 2023Discrete Diffusion Modeling by Estimating the Ratios of the Data Distributioncited by 712
  12. 2024Simplified and Generalized Masked Diffusion for Discrete Datacited by 606
27 more
  1. 2025Mean Flows for One-step Generative Modelingcited by 524
  2. 2023Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusioncited by 448
  3. 2022A Continuous Time Framework for Discrete Denoising Modelscited by 437
  4. 2023Improved Techniques for Training Consistency Modelscited by 430
  5. 2023Analyzing and Improving the Training Dynamics of Diffusion Modelscited by 396
  6. 2013One Billion Word Benchmark for Measuring Progress in Statistical Language Modelingcited by 302
  7. 2024Simplifying, Stabilizing and Scaling Continuous-Time Consistency Modelscited by 276
  8. 2022Continuous diffusion for categorical datacited by 202
  9. 2025A General Framework for Inference-time Scaling and Steering of Diffusion Modelscited by 201
  10. 2020MoFlow: An Invertible Flow Model for Generating Molecular Graphscited by 183
  11. 2022Score-based Continuous-time Discrete Diffusion Modelscited by 167
  12. 2024Simple Guidance Mechanisms for Discrete Diffusion Modelscited by 148
  13. 2022Concrete Score Matching: Generalized Score Matching for Discrete Datacited by 144
  14. 2024Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decodingcited by 127
  15. 2025The Diffusion Dualitycited by 124
  16. 2025Inductive Moment Matchingcited by 107
  17. 2025Improved Mean Flows: On the Challenges of Fastforward Generative Modelscited by 102
  18. 2023Graph Generation with Diffusion Mixturecited by 52
  19. 2024Distillation of Discrete Diffusion through Dimensional Correlationscited by 46
  20. 2025ParallelBench: Understanding the Trade-offs of Parallel Decoding in Diffusion LLMscited by 42
  21. 2021Top-N: Equivariant set and graph generation without exchangeabilitycited by 36
  22. 2025Scaling Behavior of Discrete Diffusion Language Modelscited by 32
  23. 2025Test-time scaling of diffusions with flow mapscited by 15
  24. 2025Modeling Microenvironment Trajectories on Spatial Transcriptomics with NicheFlowcited by 7
  25. 2025Flow Matching for Tabular Data Synthesiscited by 6
  26. 2025PairFlow: Closed-Form Source-Target Coupling for Few-Step Generation in Discrete Flow Modelscited by 4
  27. 2025Generative AI models capture realistic sea-ice evolution from days to decadescited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 37.

37 papers.

Sort:

By area:

  1. 2026ELF: Embedded Language Flowscited by 27
  2. 2026Discrete Flow Mapscited by 23
  3. 2026Continuous Diffusion Scales Competitively with Discrete Diffusion for Languagecited by 13
  4. 2026Self-conditioned Flow Map Language Models via Fixed-point Flowscited by 9
  5. 2026Beyond Single Tokens: Distilling Discrete Diffusion Models via Discrete MMDcited by 8
  6. 2026How to Train Your Latent Diffusion Language Model Jointly With the Latent Spacecited by 8
  7. 2026Posterior Refinement: Fast Language Generation via Any-Order Flow Mapscited by 8
  8. 2026Scaling Categorical Flow Mapscited by 6
  9. 2026Kernel-Gradient Drifting Modelscited by 6
  10. 2026Hacking Generative Perplexity: Why Unconditional Text Evaluation Needs Distributional Metricscited by 6
  11. 2026CoBit: Language Modeling with Bitstream Diffusioncited by 4
  12. 2026CountsDiff: A Diffusion Model on the Natural Numbers for Generation and Imputation of Count-Based Datacited by 2
25 more
  1. 2026Masked Language Flow Modelscited by 2
  2. 2026ConvergeFlow: Language Flow with Provable Convergence to Token Embeddingscited by 2
  3. 2026Coupling Models for One-Step Discrete Generationcited by 1
  4. 2026Few-step Cofolding with All-Atom Flow Mapscited by 1
  5. 2026BFMT: Enhancing Search Capabilities of Tree Sampler via Bootstrap Flow-Map Treecited by 1
  6. 2026Multi-Mask Diffusion Language Models for Few-Step Generationcited by 1
  7. 2026Expanding Flow Mapscited by 1
  8. 2026FluxLite: Inference-Time Proposal Control for Discrete Diffusion Modelscited by 1
  9. 2026Sampling from Flow Language Models via Marginal-Conditioned Bridgescited by 0
  10. 2026Drifting Objectives for Refining Discrete Diffusion Language Modelscited by 0
  11. 2026Logit-Coordinate Generative Models for Mixed Continuous-Categorical Tabular Datacited by 0
  12. 2026From Interface to Inference: Eliciting Any-Order Inference from Any-Order Modelscited by 0
  13. 2026Gromov-Monge Flow Matching for Equivariant Graph Generationcited by 0
  14. 2026From topology learning to graph generation: A unifying perspectivecited by 0
  15. 2026Embedded Graph Flows for Categorical Graph Generationcited by 0
  16. 2026How to Guide Your Language Flowcited by 0
  17. 2026Parallelism, critical windows, and separations among diffusion language modelscited by 0
  18. 2026Stochastic Flow Map for Count Datacited by 0
  19. 2026Partially Observed Sparse Graphs: The Unknown Sampling Rate is a Tail Indexcited by 0
  20. 2026WTF?! Simulation-Free Reinforcement Learning with Wasserstein-Tilted Flow Mapscited by 0
  21. 2026Acceleration of Diffusion Language Model through Discrete Average Generatorcited by 0
  22. 2026Distribution Matching Distillation for Continuous Diffusion Language Modelscited by 0
  23. 2026Gumbel Straight Flow: Distilling Autoregressive Models into One-step Flow Mapscited by 0
  24. 2026Clock Diffusion: Efficient Semi-Autoregressive Continuous Diffusion Language Modelscited by 0
  25. 2026Unrolled Flow Models for Reasoningcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Simplex-to-Euclidean Bijections for Categorical Flow Matching
  2. 2026Path-Guided Flow Matching for Dataset Distillation
  3. 2024Minibatch Optimal Transport and Perplexity Bound Estimation in Discrete Flow Matching
  4. 2025Diff2Flow: Training Flow Matching Models via Diffusion Model Alignment
  5. 2025Shortcutting Pre-trained Flow Matching Diffusion Models is Almost Free Lunch
  6. 2026Flow Map Learning via Nongradient Vector Flow
  7. 2026Cascaded Flow Matching for Heterogeneous Tabular Data with Mixed-Type Features
  8. 2025Branching Flows: Discrete, Continuous, and Manifold Flow Matching with Splits and Deletions