Parallelism, critical windows, and separations among diffusion language models

arXiv:2609.20539 · cs.LG, cs.DS, math.ST, stat.ML, stat.TH · Submitted 2026-09-17 · Read on arXiv

cs.LG, cs.DS, math.ST, stat.ML, stat.TH

Submitted: 2026-09-17

Updated: 2026-09-18

Comments: 90 pages

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Diffusion Model — 28× in this paper · explained in 8 episodes
• Diffusion Models — 27× in this paper · explained in 6 episodes
• Query Complexity — 15× in this paper · explained in 2 episodes
• Accuracy — 10× in this paper · explained in 1 episode
• Decode — 3× in this paper · explained in 2 episodes
• Generative Modeling — 3× in this paper · explained in 3 episodes
• Hamming Distance — 3× in this paper · explained in 2 episodes
• Convergence Guarantees — 2× in this paper · explained in 3 episodes
• Diffusion Processes — 2× in this paper · explained in 2 episodes
• Fisher Information — 2× in this paper · explained in 3 episodes
• Ornstein–Uhlenbeck Process — 2× in this paper · explained in 3 episodes
• Adaptation — 1× in this paper · explained in 1 episode
• Adaptive Algorithm — 1× in this paper · explained in 1 episode
• Adaptive Sampling — 1× in this paper · explained in 1 episode
• Diffusion Process — 1× in this paper · explained in 2 episodes
• Dynamical regimes — 1× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Flow Matching — 1× in this paper · explained in 8 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Generative Models — 1× in this paper · explained in 2 episodes
• Homogeneity — 1× in this paper · explained in 2 episodes
• Large Language Models (LLMs) — 1× in this paper · explained in 6 episodes
• Latent Space — 1× in this paper · explained in 7 episodes
• Score Function — 1× in this paper · explained in 4 episodes
• Symmetry Breaking — 1× in this paper · explained in 3 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Generating from Discrete Distributions Using Diffusions: Insights from Random Constraint Satisfaction Problems
• Convergence Analysis of Discrete Diffusion Model: Exact Implementation through Uniformization
• Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guarantees
• DiffusionGemma Technical Report
• Continuous diffusion for categorical data
• Sampling from Mean-Field Gibbs Measures via Diffusion Processes
• The Journey, Not the Destination: How Data Guides Diffusion Models
• ELF: Embedded Language Flows
• Vocabulary-size-independent Convergence of Discrete Diffusion Models: adjoint equations induce the right space
• Absorb and Converge: Provable Convergence Guarantee for Absorbing Discrete Diffusion Models
• Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution
• A Mathematical Introduction to Diffusion Models
• Flow Map Language Models: One-step Language Modeling via Continuous Denoising
• Error Bounds and Optimal Schedules for Masked Diffusions with Factorized Approximations
• Posterior Sampling in High Dimension via Diffusion Processes
• Large Language Diffusion Models
• Discrete Flow Matching: Convergence Guarantees Under Minimal Assumptions
• Bit-Level Discrete Diffusion with Markov Probabilistic Models: An Improved Framework with Sharp Convergence Bounds under Minimal Assumptions
• Categorical Flow Maps

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