# Acceleration of Diffusion Language Model through Discrete Average Generator

arXiv: https://arxiv.org/abs/2609.38364 · HTML: https://mlsanity.com/paper/2609.38364/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 30 of its 37 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Placed in

- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)

## Builds on (most cited first, 30 of 30)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Fast-dLLM: Training-free Acceleration of Diffusion LLM by Enabling KV Cache and Parallel Decoding](https://mlsanity.com/paper/2505.22618/) (2025)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data](https://mlsanity.com/paper/2406.03736/) (2024)
- [DeepCache: Accelerating Diffusion Models for Free](https://mlsanity.com/paper/2312.00858/) (2023)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generation](https://mlsanity.com/paper/2404.04057/) (2024)
- [The Diffusion Duality](https://mlsanity.com/paper/2506.10892/) (2025)
- [Improved Mean Flows: On the Challenges of Fastforward Generative Models](https://mlsanity.com/paper/2512.02012/) (2025)
- [Generator Matching: Generative modeling with arbitrary Markov processes](https://mlsanity.com/paper/2410.20587/) (2024)
- [Beyond Autoregression: Fast LLMs via Self-Distillation Through Time](https://mlsanity.com/paper/2410.21035/) (2024)
- [Flow Matching with General Discrete Paths: A Kinetic-Optimal Perspective](https://mlsanity.com/paper/2412.03487/) (2024)
- [One-step Latent-free Image Generation with Pixel Mean Flows](https://mlsanity.com/paper/2601.22158/) (2026)
- [Distillation of Discrete Diffusion through Dimensional Correlations](https://mlsanity.com/paper/2410.08709/) (2024)
- [Categorical Flow Maps](https://mlsanity.com/paper/2602.12233/) (2026)
- [Discrete Flow Maps](https://mlsanity.com/paper/2604.09784/) (2026)
- [Fast and Accurate Causal Parallel Decoding using Jacobi Forcing](https://mlsanity.com/paper/2512.14681/) (2025)
- [Error Analysis of Discrete Flow with Generator Matching](https://mlsanity.com/paper/2509.21906/) (2025)

## Abstract (arXiv)

Discrete diffusion models and flow matching have emerged as powerful frameworks for generative modeling over discrete state spaces, yet efficient few-step generation remains a fundamental challenge. In this work, we introduce the Discrete Average Generator, a principled extension of MeanFlow to Continuous-Time Markov Chains (CTMCs). Analogously to how MeanFlow defines an average velocity field over a time interval in continuous spaces, we define an average generator as the normalized increment of the transition kernel over a time interval. We show that this average generator satisfies a self-consistency identity, which provides the foundation for our training objective. We further develop training strategies that align with the standard training paradigm of diffusion language models while keeping the resulting objective tractable. When projected onto per-coordinate marginals, the self-consistency identity admits a closed-form expression, enabling efficient training and inference. In Potts model simulations, our objective reduces the total variation distance of the K-step sampler by up to 67%. On OpenWebText, our method achieves the lowest generative perplexity among the evaluated methods for 8 to 64 sampling steps while enabling a 16× acceleration, and achieves comparable performance to existing methods on ImageNet.