# Masked Diffusion Models are Secretly Learned-Order Autoregressive Models

arXiv: https://arxiv.org/abs/2511.19152 · HTML: https://mlsanity.com/paper/2511.19152/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 38 of its 40 references that are in the map.
- First posted on arXiv 24 Nov 2025.

## Placed in

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

## Builds on (most cited first, 30 of 38)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data](https://mlsanity.com/paper/2406.03736/) (2024)
- [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)
- [An Image is Worth 32 Tokens for Reconstruction and Generation](https://mlsanity.com/paper/2406.07550/) (2024)
- [Continuous diffusion for categorical data](https://mlsanity.com/paper/2211.15089/) (2022)
- [Train for the Worst, Plan for the Best: Understanding Token Ordering in Masked Diffusions](https://mlsanity.com/paper/2502.06768/) (2025)
- [Autoregressive Diffusion Models](https://mlsanity.com/paper/2110.02037/) (2021)
- [Masked Diffusion Models are Secretly Time-Agnostic Masked Models and Exploit Inaccurate Categorical Sampling](https://mlsanity.com/paper/2409.02908/) (2024)
- [Dirichlet Flow Matching with Applications to DNA Sequence Design](https://mlsanity.com/paper/2402.05841/) (2024)
- [Dimple: Discrete Diffusion Multimodal Large Language Model with Parallel Decoding](https://mlsanity.com/paper/2505.16990/) (2025)
- [Path Planning for Masked Diffusion Model Sampling](https://mlsanity.com/paper/2502.03540/) (2025)
- [Generalized Interpolating Discrete Diffusion](https://mlsanity.com/paper/2503.04482/) (2025)
- [TabDiff: a Mixed-type Diffusion Model for Tabular Data Generation](https://mlsanity.com/paper/2410.20626/) (2024)
- [Discrete Diffusion in Large Language and Multimodal Models: A Survey](https://mlsanity.com/paper/2506.13759/) (2025)
- [Informed Correctors for Discrete Diffusion Models](https://mlsanity.com/paper/2407.21243/) (2024)
- [Flow Matching with General Discrete Paths: A Kinetic-Optimal Perspective](https://mlsanity.com/paper/2412.03487/) (2024)
- [Muddit: Liberating Generation Beyond Text-to-Image with a Unified Discrete Diffusion Model](https://mlsanity.com/paper/2505.23606/) (2025)

## Built on by (most cited first, 3 of 3)

- [DiBS: Diffusion-Informed Branch Selection](https://mlsanity.com/paper/2606.06518/) (2026)
- [Induction in Both Directions: A Mechanistic Analysis of In-Context Learning in Masked Diffusion Language Models](https://mlsanity.com/paper/2607.15893/) (2026)
- [UNIFUSION: Adapting Autoregressive Language Models into Discrete Diffusion under a Unified Reverse-Rate Objective](https://mlsanity.com/paper/2607.24507/) (2026)

## Abstract (arXiv)

Masked Diffusion Models (MDMs) have emerged as one of the most promising paradigms for generative modeling over discrete domains. It is known that MDMs effectively train to decode tokens in a random order, and that this ordering has significant performance implications in practice. This observation raises a fundamental question: can we design a training framework that optimizes for a favorable decoding order? We answer this in the affirmative, showing that the continuous-time variational objective of MDMs, when equipped with multivariate noise schedules, can identify and optimize for a decoding order during training. We establish a direct correspondence between decoding order and the multivariate noise schedule and show that this setting breaks invariance of the MDM objective to the noise schedule. Furthermore, we prove that the MDM objective decomposes precisely into a weighted auto-regressive losses over these orders, which establishes them as auto-regressive models with learnable orders.