# Distillation of Discrete Diffusion through Dimensional Correlations

arXiv: https://arxiv.org/abs/2410.08709 · HTML: https://mlsanity.com/paper/2410.08709/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 53 of its 75 references that are in the map.
- First posted on arXiv 11 Oct 2024.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 53)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [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)
- [A Call for Clarity in Reporting BLEU Scores](https://mlsanity.com/paper/1804.08771/) (2018)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)

## Built on by (most cited first, 30 of 48)

- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [A Survey on Diffusion Language Models](https://mlsanity.com/paper/2508.10875/) (2025)
- [Discrete Diffusion in Large Language and Multimodal Models: A Survey](https://mlsanity.com/paper/2506.13759/) (2025)
- [Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithms](https://mlsanity.com/paper/2502.00234/) (2025)
- [KLASS: KL-Guided Fast Inference in Masked Diffusion Models](https://mlsanity.com/paper/2511.05664/) (2025)
- [Categorical Flow Maps](https://mlsanity.com/paper/2602.12233/) (2026)
- [Discrete Flow Maps](https://mlsanity.com/paper/2604.09784/) (2026)
- [Breaking AR's Sampling Bottleneck: Provable Acceleration via Diffusion Language Models](https://mlsanity.com/paper/2505.21400/) (2025)
- [Beyond Masked and Unmasked: Discrete Diffusion Models via Partial Masking](https://mlsanity.com/paper/2505.18495/) (2025)
- [Variational Autoencoding Discrete Diffusion with Enhanced Dimensional Correlations Modeling](https://mlsanity.com/paper/2505.17384/) (2025)
- [ReDi: Rectified Discrete Flow](https://mlsanity.com/paper/2507.15897/) (2025)
- [Self-conditioned Flow Map Language Models via Fixed-point Flows](https://mlsanity.com/paper/2607.00714/) (2026)
- [Beyond Single Tokens: Distilling Discrete Diffusion Models via Discrete MMD](https://mlsanity.com/paper/2603.20155/) (2026)
- [Self-Speculative Masked Diffusions](https://mlsanity.com/paper/2510.03929/) (2025)
- [Breaking the Factorization Barrier in Diffusion Language Models](https://mlsanity.com/paper/2603.00045/) (2026)
- [Demystifying MaskGIT Sampler and Beyond: Adaptive Order Selection in Masked Diffusion](https://mlsanity.com/paper/2510.04525/) (2025)
- [How Efficient Are Diffusion Language Models? A Critical Examination of Efficiency Evaluation Practices](https://mlsanity.com/paper/2510.18480/) (2025)
- [DUEL: Exact Likelihood for Masked Diffusion via Deterministic Unmasking](https://mlsanity.com/paper/2603.01367/) (2026)
- [IDLM: Inverse-distilled Diffusion Language Models](https://mlsanity.com/paper/2602.19066/) (2026)
- [Scaling Categorical Flow Maps](https://mlsanity.com/paper/2605.07820/) (2026)
- [Partition Generative Modeling: Masked Modeling Without Masks](https://mlsanity.com/paper/2505.18883/) (2025)
- [Soft-Di[M]O: Improving One-Step Discrete Image Generation with Soft Embeddings](https://mlsanity.com/paper/2509.22925/) (2025)
- [Dimathtt[M]O: Distilling Masked Diffusion Models into One-step Generator](https://mlsanity.com/paper/2503.15457/) (2025)
- [PairFlow: Closed-Form Source-Target Coupling for Few-Step Generation in Discrete Flow Models](https://mlsanity.com/paper/2512.20063/) (2025)
- [Discrete diffusion samplers and bridges: Off-policy algorithms and applications in latent spaces](https://mlsanity.com/paper/2602.05961/) (2026)
- [Drifting Objectives for Refining Discrete Diffusion Language Models](https://mlsanity.com/paper/2605.19470/) (2026)
- [Simplex Relaxation for Discrete Diffusion](https://mlsanity.com/paper/2608.10615/) (2026)
- [UniCMs: A Unified Consistency Model For Efficient Multimodal Generation and Understanding](https://mlsanity.com/paper/2502.05415/) (2025)
- [Infinite Mask Diffusion for Few-Step Distillation](https://mlsanity.com/paper/2605.10518/) (2026)
- [One-Step Distillation of Discrete Diffusion Image Generators via Fixed-Point Iteration](https://mlsanity.com/paper/2605.21484/) (2026)

## Abstract (arXiv)

Diffusion models have demonstrated exceptional performances in various fields of generative modeling, but suffer from slow sampling speed due to their iterative nature. While this issue is being addressed in continuous domains, discrete diffusion models face unique challenges, particularly in capturing dependencies between elements (e.g., pixel relationships in image, sequential dependencies in language) mainly due to the computational cost of processing high-dimensional joint distributions. In this paper, (i) we propose "mixture" models for discrete diffusion that are capable of treating dimensional correlations while remaining scalable, and (ii) we provide a set of loss functions for distilling the iterations of existing models. Two primary theoretical insights underpin our approach: First, conventional models with element-wise independence can well approximate the data distribution, but essentially require it many sampling steps. Second, our loss functions enable the mixture models to distill such many-step conventional models into just a few steps by learning the dimensional correlations. Our experimental results show the effectiveness of the proposed method in distilling pretrained discrete diffusion models across image and language domains. The code used in the paper is available at https://github.com/sony/di4c .