mlsanityData to 7 Oct 2026

Discrete Diffusion Models via Evolving Variational Autoregressive Networks

arXiv 2609.27306 ↗First posted 23 Sep 2026cs.LG cond-mat.dis-nn stat.MLcited by 0

On the map: Diffusion models → Diffusion foundations and sampling also fits: Flow matching, time series and science

Abstract (arXiv)

Conventional score-based diffusion models learn scores without representing normalized densities, whereas tractable normalized models support both sampling and direct likelihood evaluation. A recent tensor-network approach provides such a representation but is largely restricted to low-dimensional lattices. Here we introduce a discrete diffusion model that parameterizes normalized probability distributions using variational autoregressive networks. Explicit Markov jump operators govern the forward noising and reverse denoising dynamics, extending discrete diffusion models with normalized distributions to spin systems on higher-dimensional lattices. We apply this framework to the two- and three-dimensional Ising models across ordered, critical, and disordered regimes, accurately computing thermodynamic quantities including free energy, energy, and magnetization. We further integrate the framework with Monte Carlo sampling, using adaptive diffusion steps to maintain high acceptance rates even at low temperatures while enhancing sample diversity. These results establish a neural-network framework for the discrete diffusion model with normalized probability distributions.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 37 of its 61 references that are in the map. First posted on arXiv 23 Sep 2026.

Builds on

37 of 61 references.

Closest ancestors · 15

Same direction, newest first

  1. 2026Accelerating Discrete Diffusion Models with Parallel-In-Time Sampling1 Jul
  2. 2026From Independent to Correlated Diffusion: Generalized Generative Modeling with Probabilistic Computers30 Mar
  3. 2025MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Control14 Aug
  4. 2025Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physics12 Feb
  5. 2025Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithms1 Feb
  6. 2024Discrete generative diffusion models without stochastic differential equations: a tensor network approach15 Jul
  7. 2023Accelerating Markov Chain Monte Carlo sampling with diffusion models4 Sep
  8. 2022Score-based Continuous-time Discrete Diffusion Models30 Nov
  9. 2022Diffusion Models: A Comprehensive Survey of Methods and Applications2 Sep
  10. 2022A Continuous Time Framework for Discrete Denoising Models30 May
  11. 2021Conditional Image Generation with Score-Based Diffusion Models26 Nov
  12. 2021Structured Denoising Diffusion Models in Discrete State-Spaces7 Jul
3 more
  1. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  2. 2021Cascaded Diffusion Models for High Fidelity Image Generation30 May
  3. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 22

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  3. 2023Discrete Diffusion Modeling by Estimating the Ratios of the Data Distributioncited by 712
  4. 2025Block Diffusion: Interpolating Between Autoregressive and Diffusion Language Modelscited by 385
  5. 2015MADE: Masked Autoencoder for Distribution Estimationcited by 306
  6. 2023Protein Design with Guided Discrete Diffusioncited by 154
  7. 2018A high-bias, low-variance introduction to Machine Learning for physicistscited by 108
  8. 2018Solving Statistical Mechanics Using Variational Autoregressive Networkscited by 99
  9. 2024Fine-Tuning Discrete Diffusion Models via Reward Optimization with Applications to DNA and Protein Designcited by 72
  10. 2019Deep autoregressive models for the efficient variational simulation of many-body quantum systemscited by 64
  11. 2025Discrete Diffusion in Large Language and Multimodal Models: A Surveycited by 61
  12. 2024Diffusion Models for Audio Restorationcited by 32
10 more
  1. 2023ArchiSound: Audio Generation with Diffusioncited by 20
  2. 2022Neural-network solutions to stochastic reaction networkscited by 8
  3. 2026When to Commit? Towards Variable-Size Self-Contained Blocks for Discrete Diffusion Language Modelscited by 7
  4. 2025Performance of machine-learning-assisted Monte Carlo in sampling from simple statistical physics modelscited by 5
  5. 2026Markov Chain Monte Carlo with Diffusion Pathscited by 4
  6. 2025Demonstrating Real Advantage of Machine-Learning-Enhanced Monte Carlo for Combinatorial Optimizationcited by 3
  7. 2025Tracking large chemical reaction networks and rare events by neural networkscited by 3
  8. 2026Steering Without Breaking: Mechanistically Informed Interventions for Discrete Diffusion Language Modelscited by 2
  9. 2026Scalable Physics-Inspired Transformers for Spin Glassescited by 2
  10. 2026Leveraging Pretrained Language Models as Energy Functions for Glauber Dynamics Text Diffusioncited by 1

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