# Sequential Data Generation with Groupwise Diffusion Process

arXiv: https://arxiv.org/abs/2310.01400 · HTML: https://mlsanity.com/paper/2310.01400/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 33 of its 37 references that are in the map.
- First posted on arXiv 2 Oct 2023.

## Placed in

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

## Builds on (most cited first, 30 of 33)

- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (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)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Plug-and-Play Diffusion Features for Text-Driven Image-to-Image Translation](https://mlsanity.com/paper/2211.12572/) (2022)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Diffusion Models already have a Semantic Latent Space](https://mlsanity.com/paper/2210.10960/) (2022)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Perception Prioritized Training of Diffusion Models](https://mlsanity.com/paper/2204.00227/) (2022)
- [Rectified Flow: A Marginal Preserving Approach to Optimal Transport](https://mlsanity.com/paper/2209.14577/) (2022)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Dual Diffusion Implicit Bridges for Image-to-Image Translation](https://mlsanity.com/paper/2203.08382/) (2022)
- [Autoregressive Diffusion Models](https://mlsanity.com/paper/2110.02037/) (2021)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [Soft Diffusion: Score Matching for General Corruptions](https://mlsanity.com/paper/2209.05442/) (2022)
- [Blurring Diffusion Models](https://mlsanity.com/paper/2209.05557/) (2022)
- [NSML: Meet the MLaaS platform with a real-world case study](https://mlsanity.com/paper/1810.09957/) (2018)
- [A Deep and Tractable Density Estimator](https://mlsanity.com/paper/1310.1757/) (2013)
- [NSML: A Machine Learning Platform That Enables You to Focus on Your Models](https://mlsanity.com/paper/1712.05902/) (2017)

## Built on by (most cited first, 5 of 5)

- [Autoregressive Diffusion Transformer for Text-to-Speech Synthesis](https://mlsanity.com/paper/2406.05551/) (2024)
- [GUD: Generation with Unified Diffusion](https://mlsanity.com/paper/2410.02667/) (2024)
- [ADiff4TPP: Asynchronous Diffusion Models for Temporal Point Processes](https://mlsanity.com/paper/2504.20411/) (2025)
- [Applications of Explainable artificial intelligence in Earth system science](https://mlsanity.com/paper/2406.11882/) (2024)
- [Stable Autoregressive Speech Generation with Low-Frame-Rate High-Dimensional Continuous Tokens](https://mlsanity.com/paper/2607.29363/) (2026)

## Abstract (arXiv)

We present the Groupwise Diffusion Model (GDM), which divides data into multiple groups and diffuses one group at one time interval in the forward diffusion process. GDM generates data sequentially from one group at one time interval, leading to several interesting properties. First, as an extension of diffusion models, GDM generalizes certain forms of autoregressive models and cascaded diffusion models. As a unified framework, GDM allows us to investigate design choices that have been overlooked in previous works, such as data-grouping strategy and order of generation. Furthermore, since one group of the initial noise affects only a certain group of the generated data, latent space now possesses group-wise interpretable meaning. We can further extend GDM to the frequency domain where the forward process sequentially diffuses each group of frequency components. Dividing the frequency bands of the data as groups allows the latent variables to become a hierarchical representation where individual groups encode data at different levels of abstraction. We demonstrate several applications of such representation including disentanglement of semantic attributes, image editing, and generating variations.