mlsanityData to 14 Oct 2026

The data geometry of masking diffusion: Certified-optimal schedules via unmasking growth complexity

arXiv 2608.13520 ↗First posted 13 Aug 2026cs.LG cs.AI cs.ITcited by 9

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Abstract (arXiv)

We study masking diffusion for discrete sampling and introduce a path-resolved measure of data geometry called the unmasking growth complexity (textsfUGCxspace). Its local increments directly control Kullback--Leibler (KL) discretization error, yielding a unified analysis of Bernoulli-subset and fixed-cardinality unmasking schemes. In log-reveal-odds coordinates, this structure yields optimized single-block and multi-block schedules, and quantifies the gains from adapting computational effort to data geometry. Crucially, we show how textsfUGCxspace increments can be estimated from samples via KL increments along coupled reveal trajectories. This leads to certified-optimal samplers that achieve a prescribed KL error with high probability and iteration complexity within a constant factor of the corresponding oracle procedure. Collapsing the ugc path yields the aggregate textsfUGCxspace mass, which connects to classical multivariate dependence measures and complexity measures from previous analyses of discrete diffusion. In the fine-partition limit, the squared integral of the square-root textsfUGCxspace density determines the sharp leading-order optimal Euler discretization error. Examples exhibit substantial dimension-dependent gains over coarse schedules, including widetildeOmega(√d) improvements achievable with a constant number of adaptively placed blocks.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 30 of its 53 references that are in the map. First posted on arXiv 13 Aug 2026.

Builds on

30 of 53 references.

References · 30

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  5. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  6. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,719
  7. 2022MaskGIT: Masked Generative Image Transformercited by 1,099
  8. 2022Diffusion Models in Vision: A Surveycited by 1,015
  9. 2025Large Language Diffusion Modelscited by 912
  10. 2024Simple and Effective Masked Diffusion Language Modelscited by 848
  11. 2023Discrete Diffusion Modeling by Estimating the Ratios of the Data Distributioncited by 745
  12. 2023Muse: Text-To-Image Generation via Masked Generative Transformerscited by 648
18 more
  1. 2024Simplified and Generalized Masked Diffusion for Discrete Datacited by 626
  2. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 574
  3. 2022A Continuous Time Framework for Discrete Denoising Modelscited by 451
  4. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptionscited by 445
  5. 2022MAGVIT: Masked Generative Video Transformercited by 346
  6. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localizationcited by 235
  7. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptionscited by 219
  8. 2024MaskGCT: Zero-Shot Text-to-Speech with Masked Generative Codec Transformercited by 161
  9. 2024Diffusion Language Models Are Versatile Protein Learnerscited by 98
  10. 2024An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimizationcited by 73
  11. 2024How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Frameworkcited by 48
  12. 2025Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithmscited by 47
  13. 2019Quantifying High-order Interdependencies via Multivariate Extensions of the Mutual Informationcited by 30
  14. 2025Optimal Inference Schedules for Masked Diffusion Modelscited by 25
  15. 2025Breaking AR's Sampling Bottleneck: Provable Acceleration via Diffusion Language Modelscited by 23
  16. 2025Absorb and Converge: Provable Convergence Guarantee for Absorbing Discrete Diffusion Modelscited by 20
  17. 2025Discrete Diffusion Models: Novel Analysis and New Sampler Guaranteescited by 20
  18. 2026Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guaranteescited by 19

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 9.

9 papers.

  1. 2026Provably adaptive sampling with uniform and remasking discrete diffusion modelscited by 4
  2. 2026ConvergeFlow: Language Flow with Provable Convergence to Token Embeddingscited by 2
  3. 2026The information geometry of product-reference discrete diffusion: Interaction growth complexity and optimal schedulingcited by 2
  4. 2026Conditional Total Correlation and the Serial Depth of Adaptive Parallel Samplingcited by 1
  5. 2026Parallelism, critical windows, and separations among diffusion language modelscited by 1
  6. 2026Schedule optimization for tau-leaping in masked discrete diffusioncited by 0
  7. 2026Simple Diffusion Language Models Are More Effective Few-Step Generators Than Reportedcited by 0
  8. 2026Counterfactual Probing for Parallel Unmasking with Hidden Forest Structurecited by 0
  9. 2026Sample complexity bounds for categorical Markov random fields via Discrete Diffusionscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Denoising growth complexity: Data geometry and certified schedules for diffusion sampling
  2. 2025Error Bounds and Optimal Schedules for Masked Diffusions with Factorized Approximations
  3. 2026Understanding Parallel Samplers in Masked Diffusion via Random Walks on Graphs
  4. 2025The Cosine Schedule is Fisher-Rao-Optimal for Masked Discrete Diffusion Models
  5. 2026VGB for Masked Diffusion Model: Efficient Test-time Scaling for Reward Satisfaction and Sample Editing
  6. 2026Transformer-Based Masked Diffusion Models Provably Learn Distributions with Latent Structure
  7. 2025Why Masking Diffusion Works: Condition on the Jump Schedule for Improved Discrete Diffusion
  8. 2026DUEL: Exact Likelihood for Masked Diffusion via Deterministic Unmasking