mlsanityData to 14 Oct 2026

Jumping up and down: Denoiser diffusion models for discrete ordinal data

arXiv 2610.02754 ↗First posted 2 Oct 2026cs.LG stat.MEcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Diffusion models are highly developed in continuous spaces for image and video domains. Recently, major advances have been made for discrete diffusion models for categorical data, specifically in the language domain. In contrast, diffusion models for discrete integer-valued data are less developed, despite the prevalence of this modality, ranging from images and music to gene counts. We introduce Jumping Up and Down (JUD)---a new family of denoiser-based diffusion models for discrete ordinal data. This is the first family of diffusion models for ordinal data which centers around training denoisers, which at the same time allows for bi-directional (up and down) perturbations of the data. The simplicity of the training objective, combined with the flexibility of bi-directional perturbations, leads us to obtain competitive results across different data modalities.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 40 of its 45 references that are in the map. First posted on arXiv 2 Oct 2026.

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40 of 45 references.

Closest ancestors · 17

Same direction, newest first

  1. 2026Binomial flows: Denoising and flow matching for discrete ordinal data1 May
  2. 2026Blind denoising diffusion models and the blessings of dimensionality10 Feb
  3. 2025ItDPDM: Information-Theoretic Discrete Poisson Diffusion Model8 May
  4. 2025Discrete Spatial Diffusion: Intensity-Preserving Diffusion Modeling3 May
  5. 2025Is Noise Conditioning Necessary for Denoising Generative Models?18 Feb
  6. 2025Sampling Binary Data by Denoising through Score Functions1 Feb
  7. 2024Multistep Distillation of Diffusion Models via Moment Matching6 Jun
  8. 2024Bridging discrete and continuous state spaces: Exploring the Ehrenfest process in time-continuous diffusion models6 May
  9. 2023Trans-Dimensional Generative Modeling via Jump Diffusion Models25 May
  10. 2023Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces18 May
  11. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  12. 2022A Continuous Time Framework for Discrete Denoising Models30 May
5 more
  1. 2021Structured Denoising Diffusion Models in Discrete State-Spaces7 Jul
  2. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  4. 2020Denoising Diffusion Implicit Models6 Oct
  5. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 23

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  3. 2023Discrete Diffusion Modeling by Estimating the Ratios of the Data Distributioncited by 745
  4. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 574
  5. 2024Discrete Flow Matchingcited by 317
  6. 2022Concrete Score Matching: Generalized Score Matching for Discrete Datacited by 148
  7. 2024Unlocking Guidance for Discrete State-Space Diffusion and Flow Modelscited by 129
  8. 2024Generator Matching: Generative modeling with arbitrary Markov processescited by 86
  9. 2026ELF: Embedded Language Flowscited by 45
  10. 2023Sampling, Diffusions, and Stochastic Localizationcited by 40
  11. 2025Continuously Augmented Discrete Diffusion model for Categorical Generative Modelingcited by 34
  12. 2026Language Modeling with Hyperspherical Flowscited by 22
11 more
  1. 2025Equilibrium Matching: Generative Modeling with Implicit Energy-Based Modelscited by 21
  2. 2025Beyond Masked and Unmasked: Discrete Diffusion Models via Partial Maskingcited by 20
  3. 2023Learning to Jump: Thinning and Thickening Latent Counts for Generative Modelingcited by 18
  4. 2025Learning normalized image densities via dual score matchingcited by 18
  5. 2023RecFusion: A Binomial Diffusion Process for 1D Data for Recommendationcited by 7
  6. 2026Lingshu-Cell: A generative cellular world model for transcriptome modeling toward virtual cellscited by 6
  7. 2026Count Bridges enable Modeling and Deconvolving Transcriptomic Datacited by 4
  8. 2026Flow Matching for Count Datacited by 3
  9. 2026ScDiVa: Masked Discrete Diffusion for Joint Modeling of Single-Cell Identity and Expressioncited by 1
  10. 2026Variable-Length Generative Protein Design via Generalized Poisson Flowcited by 1
  11. 2026Stochastic Flow Map for Count Datacited by 1

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  6. 2026CDMD: A Cross-Dataset Mixed-Type Diffusion Model for Tabular Data
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