mlsanityData to 7 Oct 2026

Set Diffusion: Interpolating Token Orderings Between Autoregression and Diffusion for Fast and Flexible Decoding

arXiv 2607.01775 ↗First posted 2 Jul 2026cs.LGcited by 2

On the map: Diffusion models → Discrete and text diffusion

Abstract (arXiv)

Discrete diffusion models have steadily improved in quality relative to autoregressive (AR) models. However, these models are normally constrained to fixed-length generation and do not support key-value (KV) caching. Block diffusion partially bridges diffusion and AR by generating token blocks left-to-right, but its fixed-size sequential blocks limit decoding flexibility and parallelism. Here, we present a new class of language models, set diffusion, comprised of (i) a likelihood parameterization that factorizes over flexible-position, flexible-length token sets and (ii) a set-causal diffusion architecture that supports KV cache updates after every inference step. By factorizing over token sets instead of fixed-size blocks, tokens can be decoded in arbitrarily-ordered sets, including sliding-window sets, enabling faster inference and support for any-order decoding. Set diffusion achieves better speed-quality tradeoffs on mathematical reasoning, summarization, and unconditional generation compared to prior diffusion language models while offering stronger infilling performance than block diffusion. We provide the code, along with the model weights and blog post on the project page: https://m-arriola.com/setdlms/

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Placed in Discrete and text diffusion, one of 14 directions in Diffusion models. Builds on 54 of its 70 references that are in the map. First posted on arXiv 2 Jul 2026.

Builds on

54 of 70 references.

Closest ancestors · 24

Same direction, newest first

  1. 2026DUEL: Exact Likelihood for Masked Diffusion via Deterministic Unmasking2 Mar
  2. 2026Learn from Your Mistakes: Self-Correcting Masked Diffusion Models12 Feb
  3. 2026Stop Training for the Worst: Progressive Unmasking Accelerates Masked Diffusion Training10 Feb
  4. 2026Deferred Commitment Decoding for Diffusion Language Models5 Jan
  5. 2025WeDLM: Reconciling Diffusion Language Models with Standard Causal Attention for Fast Inference28 Dec
  6. 2025Sparse-LaViDa: Sparse Multimodal Discrete Diffusion Language Models16 Dec
  7. 2025Sequential Diffusion Language Models28 Sep
  8. 2025Fast and Fluent Diffusion Language Models via Convolutional Decoding and Rejective Fine-tuning18 Sep
  9. 2025Any-Order Flexible Length Masked Diffusion31 Aug
  10. 2025Diffusion Beats Autoregressive in Data-Constrained Settings21 Jul
  11. 2025The Diffusion Duality12 Jun
  12. 2025dKV-Cache: The Cache for Diffusion Language Models21 May
12 more
  1. 2025Remasking Discrete Diffusion Models with Inference-Time Scaling1 Mar
  2. 2025Train for the Worst, Plan for the Best: Understanding Token Ordering in Masked Diffusions10 Feb
  3. 2024Scaling up Masked Diffusion Models on Text24 Oct
  4. 2024Scaling Diffusion Language Models via Adaptation from Autoregressive Models23 Oct
  5. 2024Masked Diffusion Models are Secretly Time-Agnostic Masked Models and Exploit Inaccurate Categorical Sampling4 Sep
  6. 2024Simple and Effective Masked Diffusion Language Models11 Jun
  7. 2024Simplified and Generalized Masked Diffusion for Discrete Data6 Jun
  8. 2024Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data6 Jun
  9. 2023AR-Diffusion: Auto-Regressive Diffusion Model for Text Generation16 May
  10. 2022Text Generation with Diffusion Language Models: A Pre-training Approach with Continuous Paragraph Denoise22 Dec
  11. 2022SSD-LM: Semi-autoregressive Simplex-based Diffusion Language Model for Text Generation and Modular Control31 Oct
  12. 2021Autoregressive Diffusion Models5 Oct

Other references · 30

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2019Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformercited by 14,491
  4. 2021Training Verifiers to Solve Math Word Problemscited by 9,743
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  6. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  7. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  8. 2019Transformer-XL: Attentive Language Models Beyond a Fixed-Length Contextcited by 1,830
  9. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  10. 2017Get To The Point: Summarization with Pointer-Generator Networkscited by 1,281
  11. 2015Teaching Machines to Read and Comprehendcited by 1,039
  12. 2022Diffusion-LM Improves Controllable Text Generationcited by 1,006
18 more
  1. 2019Text Summarization with Pretrained Encoderscited by 553
  2. 2021MAUVE: Measuring the Gap Between Neural Text and Human Text using Divergence Frontierscited by 466
  3. 2016A Corpus and Evaluation Framework for Deeper Understanding of Commonsense Storiescited by 413
  4. 2025Fast-dLLM: Training-free Acceleration of Diffusion LLM by Enabling KV Cache and Parallel Decodingcited by 404
  5. 2013One Billion Word Benchmark for Measuring Progress in Statistical Language Modelingcited by 302
  6. 2023Understanding Diffusion Objectives as the ELBO with Simple Data Augmentationcited by 293
  7. 2024Flex Attention: A Programming Model for Generating Optimized Attention Kernelscited by 180
  8. 2022Score-based Continuous-time Discrete Diffusion Modelscited by 167
  9. 2013A Deep and Tractable Density Estimatorcited by 67
  10. 2022Training and Inference on Any-Order Autoregressive Models the Right Waycited by 64
  11. 2023Diffusion Models With Learned Adaptive Noisecited by 50
  12. 2023InfoDiffusion: Representation Learning Using Information Maximizing Diffusion Modelscited by 48
  13. 2025Esoteric Language Models: A Family of Any-Order Diffusion LLMscited by 33
  14. 2025Attention Is All You Need for KV Cache in Diffusion LLMscited by 32
  15. 2025Learning-Order Autoregressive Models with Application to Molecular Graph Generationcited by 29
  16. 2025Reviving Any-Subset Autoregressive Models with Principled Parallel Sampling and Speculative Decodingcited by 14
  17. 2023FiLM: Fill-in Language Models for Any-Order Generationcited by 13
  18. 2023David helps Goliath: Inference-Time Collaboration Between Small Specialized and Large General Diffusion LMscited by 6

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Answer First, Reason Later: When Commitment Order Costs Accuracy in Diffusion Language Modelscited by 2
  2. 2026Clock Diffusion: Efficient Semi-Autoregressive Continuous Diffusion Language Modelscited by 0

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