# Clustering by Denoising: Latent plug-and-play diffusion for single-cell data

arXiv: https://arxiv.org/abs/2510.22835 · HTML: https://mlsanity.com/paper/2510.22835/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 66 references that are in the map.
- First posted on arXiv 26 Oct 2025.

## Builds on (most cited first, 21 of 21)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [From Louvain to Leiden: guaranteeing well-connected communities](https://mlsanity.com/paper/1810.08473/) (2018)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors](https://mlsanity.com/paper/2405.18782/) (2024)
- [Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau](https://mlsanity.com/paper/1612.07471/) (2016)
- [Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction](https://mlsanity.com/paper/2403.17042/) (2024)
- [Split-and-augmented Gibbs sampler - Application to large-scale inference problems](https://mlsanity.com/paper/1804.05809/) (2018)
- [Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inference](https://mlsanity.com/paper/2304.11134/) (2023)
- [scDiffusion: conditional generation of high-quality single-cell data using diffusion model](https://mlsanity.com/paper/2401.03968/) (2024)
- [Towards Practical Plug-and-Play Diffusion Models](https://mlsanity.com/paper/2212.05973/) (2022)
- [Removal of Batch Effects using Distribution-Matching Residual Networks](https://mlsanity.com/paper/1610.04181/) (2016)
- [Empirical Bayes PCA in high dimensions](https://mlsanity.com/paper/2012.11676/) (2020)
- [Multimodal data integration and cross-modal querying via orchestrated approximate message passing](https://mlsanity.com/paper/2407.19030/) (2024)
- [Non-negative matrix factorization algorithms generally improve topic model fits](https://mlsanity.com/paper/2105.13440/) (2021)

## Abstract (arXiv)

Single-cell RNA sequencing (scRNA-seq) enables the study of cellular heterogeneity. Yet, clustering accuracy, and with it downstream analyses based on cell labels, remain challenging due to measurement noise and biological variability. In standard latent spaces (e.g., obtained through PCA), data from different cell types can be projected close together, making accurate clustering difficult. We introduce a latent plug-and-play diffusion framework that separates the observation and denoising space. This separation is operationalized through a novel Gibbs sampling procedure: the learned diffusion prior is applied in a low-dimensional latent space to perform denoising, while to steer this process, noise is reintroduced into the original high-dimensional observation space. This unique "input-space steering" ensures the denoising trajectory remains faithful to the original data structure. Our approach offers three key advantages: (1) adaptive noise handling via a tunable balance between prior and observed data; (2) uncertainty quantification through principled uncertainty estimates for downstream analysis; and (3) generalizable denoising by leveraging clean reference data to denoise noisier datasets, and via averaging, improve quality beyond the training set. We evaluate robustness on both synthetic and real single-cell genomics data. Our method improves clustering accuracy on synthetic data across varied noise levels and dataset shifts. On real-world single-cell data, our method demonstrates improved biological coherence in the resulting cell clusters, with cluster boundaries that better align with known cell type markers and developmental trajectories.