# ClusterDDPM: An EM clustering framework with Denoising Diffusion Probabilistic Models

arXiv: https://arxiv.org/abs/2312.08029 · HTML: https://mlsanity.com/paper/2312.08029/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 17 of its 28 references that are in the map.
- First posted on arXiv 13 Dec 2023.

## Placed in

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

## Builds on (most cited first, 17 of 17)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (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)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Variational Deep Embedding: An Unsupervised and Generative Approach to Clustering](https://mlsanity.com/paper/1611.05148/) (2016)
- [Unrolled Generative Adversarial Networks](https://mlsanity.com/paper/1611.02163/) (2016)
- [Conditional Image-to-Video Generation with Latent Flow Diffusion Models](https://mlsanity.com/paper/2303.13744/) (2023)
- [ClusterGAN : Latent Space Clustering in Generative Adversarial Networks](https://mlsanity.com/paper/1809.03627/) (2018)
- [Unsupervised Representation Learning from Pre-trained Diffusion Probabilistic Models](https://mlsanity.com/paper/2212.12990/) (2022)
- [Stick-Breaking Variational Autoencoders](https://mlsanity.com/paper/1605.06197/) (2016)
- [Global Context with Discrete Diffusion in Vector Quantised Modelling for Image Generation](https://mlsanity.com/paper/2112.01799/) (2021)
- [First Hitting Diffusion Models for Generating Manifold, Graph and Categorical Data](https://mlsanity.com/paper/2209.01170/) (2022)
- [GAN-EM: GAN based EM learning framework](https://mlsanity.com/paper/1812.00335/) (2018)

## Built on by (most cited first, 2 of 2)

- [DiEC: Diffusion Embedded Clustering](https://mlsanity.com/paper/2512.20905/) (2025)
- [Pro-t-VAE: Closed-Form Student's t Mixtures for Robust Prototype Discovery](https://mlsanity.com/paper/2610.14894/) (2026)

## Abstract (arXiv)

Variational autoencoder (VAE) and generative adversarial networks (GAN) have found widespread applications in clustering and have achieved significant success. However, the potential of these approaches may be limited due to VAE's mediocre generation capability or GAN's well-known instability during adversarial training. In contrast, denoising diffusion probabilistic models (DDPMs) represent a new and promising class of generative models that may unlock fresh dimensions in clustering. In this study, we introduce an innovative expectation-maximization (EM) framework for clustering using DDPMs. In the E-step, we aim to derive a mixture of Gaussian priors for the subsequent M-step. In the M-step, our focus lies in learning clustering-friendly latent representations for the data by employing the conditional DDPM and matching the distribution of latent representations to the mixture of Gaussian priors. We present a rigorous theoretical analysis of the optimization process in the M-step, proving that the optimizations are equivalent to maximizing the lower bound of the Q function within the vanilla EM framework under certain constraints. Comprehensive experiments validate the advantages of the proposed framework, showcasing superior performance in clustering, unsupervised conditional generation and latent representation learning.