# Categorical Flow Maps

arXiv: https://arxiv.org/abs/2602.12233 · HTML: https://mlsanity.com/paper/2602.12233/

## Key facts

- Cited by 44 papers in the map (data through 14 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.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)
- Knowledge distillation / [Multimodal distillation](https://mlsanity.com/distill/multimodal-distillation/)

## Builds on (most cited first, 30 of 61)

- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [One Billion Word Benchmark for Measuring Progress in Statistical Language Modeling](https://mlsanity.com/paper/1312.3005/) (2013)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024)
- [A General Framework for Inference-time Scaling and Steering of Diffusion Models](https://mlsanity.com/paper/2501.06848/) (2025)
- [Continuous diffusion for categorical data](https://mlsanity.com/paper/2211.15089/) (2022)
- [MoFlow: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/2006.10137/) (2020)
- [Score-based Continuous-time Discrete Diffusion Models](https://mlsanity.com/paper/2211.16750/) (2022)
- [Simple Guidance Mechanisms for Discrete Diffusion Models](https://mlsanity.com/paper/2412.10193/) (2024)

## Built on by (most cited first, 30 of 44)

- [ELF: Embedded Language Flows](https://mlsanity.com/paper/2605.10938/) (2026)
- [Discrete Flow Maps](https://mlsanity.com/paper/2604.09784/) (2026)
- [Continuous Diffusion Scales Competitively with Discrete Diffusion for Language](https://mlsanity.com/paper/2605.18530/) (2026)
- [Self-conditioned Flow Map Language Models via Fixed-point Flows](https://mlsanity.com/paper/2607.00714/) (2026)
- [Beyond Single Tokens: Distilling Discrete Diffusion Models via Discrete MMD](https://mlsanity.com/paper/2603.20155/) (2026)
- [How to Train Your Latent Diffusion Language Model Jointly With the Latent Space](https://mlsanity.com/paper/2605.07933/) (2026)
- [Posterior Refinement: Fast Language Generation via Any-Order Flow Maps](https://mlsanity.com/paper/2606.24773/) (2026)
- [CoBit: Language Modeling with Bitstream Diffusion](https://mlsanity.com/paper/2605.07013/) (2026)
- [Scaling Categorical Flow Maps](https://mlsanity.com/paper/2605.07820/) (2026)
- [Kernel-Gradient Drifting Models](https://mlsanity.com/paper/2605.10727/) (2026)
- [Hacking Generative Perplexity: Why Unconditional Text Evaluation Needs Distributional Metrics](https://mlsanity.com/paper/2606.08417/) (2026)
- [CountsDiff: A Diffusion Model on the Natural Numbers for Generation and Imputation of Count-Based Data](https://mlsanity.com/paper/2604.03779/) (2026)
- [Coupling Models for One-Step Discrete Generation](https://mlsanity.com/paper/2605.07193/) (2026)
- [Drifting Objectives for Refining Discrete Diffusion Language Models](https://mlsanity.com/paper/2605.19470/) (2026)
- [Masked Language Flow Models](https://mlsanity.com/paper/2606.27617/) (2026)
- [ConvergeFlow: Language Flow with Provable Convergence to Token Embeddings](https://mlsanity.com/paper/2608.23551/) (2026)
- [Few-step Cofolding with All-Atom Flow Maps](https://mlsanity.com/paper/2606.08375/) (2026)
- [Continuous Language Diffusion as a Decoder-Interface Problem](https://mlsanity.com/paper/2606.08810/) (2026)
- [BFMT: Enhancing Search Capabilities of Tree Sampler via Bootstrap Flow-Map Tree](https://mlsanity.com/paper/2607.02915/) (2026)
- [Multi-Mask Diffusion Language Models for Few-Step Generation](https://mlsanity.com/paper/2607.19686/) (2026)
- [Expanding Flow Maps](https://mlsanity.com/paper/2607.21585/) (2026)
- [From Interface to Inference: Eliciting Any-Order Inference from Any-Order Models](https://mlsanity.com/paper/2607.26504/) (2026)
- [Parallelism, critical windows, and separations among diffusion language models](https://mlsanity.com/paper/2609.20539/) (2026)
- [Stochastic Flow Map for Count Data](https://mlsanity.com/paper/2609.23290/) (2026)
- [WTF?! Simulation-Free Reinforcement Learning with Wasserstein-Tilted Flow Maps](https://mlsanity.com/paper/2609.27033/) (2026)
- [FluxLite: Inference-Time Proposal Control for Discrete Diffusion Models](https://mlsanity.com/paper/2609.35947/) (2026)
- [Sampling from Flow Language Models via Marginal-Conditioned Bridges](https://mlsanity.com/paper/2605.13681/) (2026)
- [Logit-Coordinate Generative Models for Mixed Continuous-Categorical Tabular Data](https://mlsanity.com/paper/2607.23348/) (2026)
- [Gromov-Monge Flow Matching for Equivariant Graph Generation](https://mlsanity.com/paper/2608.26961/) (2026)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)

## 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.