mlsanityData to 14 Oct 2026

Binomial flows: Denoising and flow matching for discrete ordinal data

arXiv 2605.00360 ↗First posted 1 May 2026cs.LG stat.MEcited by 1

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Flow-based generative modeling in continuous spaces exploit Tweedie's formula to express the denoiser (learned in training) as a score function (used in sampling). In contrast, this relation has been largely missing in the discrete setting where common approaches focus on learning discrete scores and rates. In this work we close this gap for discrete non-negative ordinal data by introducing Binomial flows. Our framework provides a simple recipe for training a discrete diffusion model which simultaneously denoises, samples, and estimates exact likelihoods. We verify our methodology on synthetic examples and obtain competitive results on real-world data sets.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 35 of its 45 references that are in the map. First posted on arXiv 1 May 2026.

Builds on

35 of 45 references.

Closest ancestors · 15

Same direction, newest first

  1. 2025ItDPDM: Information-Theoretic Discrete Poisson Diffusion Model8 May
  2. 2025Sampling Binary Data by Denoising through Score Functions1 Feb
  3. 2024How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Framework4 Oct
  4. 2024Discrete Diffusion Schr"odinger Bridge Matching for Graph Transformation2 Oct
  5. 2023Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces18 May
  6. 2023Diffusion Schr"odinger Bridge Matching29 Mar
  7. 2023Consistent Diffusion Models: Mitigating Sampling Drift by Learning to be Consistent17 Feb
  8. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  9. 2022A Continuous Time Framework for Discrete Denoising Models30 May
  10. 2021Structured Denoising Diffusion Models in Discrete State-Spaces7 Jul
  11. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  12. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
3 more
  1. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  2. 2020Denoising Diffusion Implicit Models6 Oct
  3. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 20

  1. 2022Flow Matching for Generative Modelingcited by 5,702
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  3. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,700
  4. 2022Building Normalizing Flows with Stochastic Interpolantscited by 995
  5. 2023Discrete Diffusion Modeling by Estimating the Ratios of the Data Distributioncited by 745
  6. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 574
  7. 2024Discrete Flow Matchingcited by 317
  8. 2024Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Designcited by 305
  9. 2024Flow Matching Guide and Codecited by 301
  10. 2013A survey of the Schr"odinger problem and some of its connections with optimal transportcited by 292
  11. 2024Unlocking Guidance for Discrete State-Space Diffusion and Flow Modelscited by 129
  12. 2019Theoretical guarantees for sampling and inference in generative models with latent diffusionscited by 97
8 more
  1. 2023Diffusion Bridge Mixture Transports, Schr"odinger Bridge Problems and Generative Modelingcited by 80
  2. 2024Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processescited by 66
  3. 2024Think While You Generate: Discrete Diffusion with Planned Denoisingcited by 63
  4. 2023Sampling, Diffusions, and Stochastic Localizationcited by 40
  5. 2025Continuously Augmented Discrete Diffusion model for Categorical Generative Modelingcited by 34
  6. 2025Beyond Masked and Unmasked: Discrete Diffusion Models via Partial Maskingcited by 20
  7. 2023Learning to Jump: Thinning and Thickening Latent Counts for Generative Modelingcited by 18
  8. 2025Categorical Schr"odinger Bridge Matchingcited by 5

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Jumping up and down: Denoiser diffusion models for discrete ordinal datacited by 0

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  1. 2026Bernoulli Flow Models: Self-Consistent Generative Modeling for Binary Data
  2. 2026A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models
  3. 2025α-Flow: A Unified Framework for Continuous-State Discrete Flow Matching Models
  4. 2022Score-based Continuous-time Discrete Diffusion Models
  5. 2026Statistical Inference via Generative Models: Flow Matching and Causal Inference
  6. 2025Bit-Level Discrete Diffusion with Markov Probabilistic Models: An Improved Framework with Sharp Convergence Bounds under Minimal Assumptions
  7. 2024Discrete vs. Continuous Trade-offs for Generative Models
  8. 2021Discrete Denoising Flows