mlsanityData to 7 Oct 2026

Deterministic Discrete Denoising

arXiv 2509.20896 ↗First posted 25 Sep 2025cs.LG nlin.CDcited by 1

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

We propose a deterministic denoising algorithm for discrete-state diffusion models. The key idea is to derandomize the generative reverse Markov chain by introducing a variant of the herding algorithm, which induces deterministic state transitions driven by weakly chaotic dynamics. It serves as a direct replacement for the stochastic denoising process, without requiring retraining or continuous state embeddings. We demonstrate consistent improvements in both efficiency and sample quality on text and image generation tasks. In addition, the proposed algorithm yields improved solutions for diffusion-based combinatorial optimization. Thus, herding-based denoising is a simple yet promising approach for enhancing the generative process of discrete diffusion models. Furthermore, our results reveal that deterministic reverse processes, well established in continuous diffusion, can also be effective in discrete state spaces.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 34 of its 60 references that are in the map. First posted on arXiv 25 Sep 2025.

Builds on

34 of 60 references.

Closest ancestors · 16

Same direction, newest first

  1. 2025Discrete Diffusion Models: Novel Analysis and New Sampler Guarantees20 Sep
  2. 2025Absorb and Converge: Provable Convergence Guarantee for Absorbing Discrete Diffusion Models2 Jun
  3. 2025Debiasing Guidance for Discrete Diffusion with Sequential Monte Carlo10 Feb
  4. 2025Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithms1 Feb
  5. 2025A General Framework for Inference-time Scaling and Steering of Diffusion Models12 Jan
  6. 2024Simple Guidance Mechanisms for Discrete Diffusion Models13 Dec
  7. 2024textitJump Your Steps: Optimizing Sampling Schedule of Discrete Diffusion Models10 Oct
  8. 2024How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Framework4 Oct
  9. 2024Convergence of Score-Based Discrete Diffusion Models: A Discrete-Time Analysis3 Oct
  10. 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization16 Feb
  11. 2022Score-based Continuous-time Discrete Diffusion Models30 Nov
  12. 2022Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioning8 Aug
4 more
  1. 2022A Continuous Time Framework for Discrete Denoising Models30 May
  2. 2021Structured Denoising Diffusion Models in Discrete State-Spaces7 Jul
  3. 2020Denoising Diffusion Implicit Models6 Oct
  4. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 18

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  2. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  3. 2015Rethinking the Inception Architecture for Computer Visioncited by 5,451
  4. 2016Improved Techniques for Training GANscited by 2,938
  5. 2025Large Language Diffusion Modelscited by 872
  6. 2024Simple and Effective Masked Diffusion Language Modelscited by 800
  7. 2023Discrete Diffusion Modeling by Estimating the Ratios of the Data Distributioncited by 712
  8. 2024Simplified and Generalized Masked Diffusion for Discrete Datacited by 606
  9. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 566
  10. 2021MAUVE: Measuring the Gap Between Neural Text and Human Text using Divergence Frontierscited by 466
  11. 2013One Billion Word Benchmark for Measuring Progress in Statistical Language Modelingcited by 302
  12. 2025LLaDA 1.5: Variance-Reduced Preference Optimization for Large Language Diffusion Modelscited by 273
6 more
  1. 2020Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instancescited by 161
  2. 2025Accelerated Sampling from Masked Diffusion Models via Entropy Bounded Unmaskingcited by 128
  3. 2025The Diffusion Dualitycited by 124
  4. 2025Generalized Interpolating Discrete Diffusioncited by 68
  5. 2023Fast Sampling via Discrete Non-Markov Diffusion Models with Predetermined Transition Timecited by 20
  6. 2024Noise-augmented Chaotic Ising Machines for Combinatorial Optimization and Samplingcited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Stratified Hazard Sampling: Minimal-Variance Event Scheduling for CTMC/DTMC Discrete Diffusion and Flow Modelscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025A Unified Approach to Analysis and Design of Denoising Markov Models
  2. 2023The Missing U for Efficient Diffusion Models
  3. 2026A Tutorial on Diffusion Theory: From Differential Equations to Diffusion Models
  4. 2026Forward-Learned Discrete Diffusion: Learning how to noise to denoise faster
  5. 2023Iterative α-(de)Blending: a Minimalist Deterministic Diffusion Model
  6. 2025Diffusion Models: A Mathematical Introduction
  7. 2023Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models
  8. 2024Think While You Generate: Discrete Diffusion with Planned Denoising