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

Dominik Meier, Shixing Yu, Sagnik Nandy, Promit Ghosal, Kyra Gan

TL;DR

The paper tackles the challenge of noisy single-cell clustering by introducing DICE, a latent plug-and-play diffusion framework that learns a diffusion prior from high-quality reference data in a low-dimensional latent space and denoises target data via input-space steering with a split Gibbs sampler. The method enables adaptive noise handling through a tunable $\rho$, provides principled uncertainty estimates for downstream analyses, and achieves generalizable denoising by transferring structure from the reference atlas. Empirically, DICE improves clustering accuracy and biological coherence on synthetic benchmarks and real scRNA-seq datasets (e.g., CITE-seq PBMCs and human fetal brain development datasets), including cross-dataset denoising and improved trajectory resolution. These results demonstrate the practical impact of combining latent diffusion priors with input-space guidance for robust, uncertainty-aware single-cell analysis and atlas construction.

Abstract

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.

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

TL;DR

The paper tackles the challenge of noisy single-cell clustering by introducing DICE, a latent plug-and-play diffusion framework that learns a diffusion prior from high-quality reference data in a low-dimensional latent space and denoises target data via input-space steering with a split Gibbs sampler. The method enables adaptive noise handling through a tunable , provides principled uncertainty estimates for downstream analyses, and achieves generalizable denoising by transferring structure from the reference atlas. Empirically, DICE improves clustering accuracy and biological coherence on synthetic benchmarks and real scRNA-seq datasets (e.g., CITE-seq PBMCs and human fetal brain development datasets), including cross-dataset denoising and improved trajectory resolution. These results demonstrate the practical impact of combining latent diffusion priors with input-space guidance for robust, uncertainty-aware single-cell analysis and atlas construction.

Abstract

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.
Paper Structure (42 sections, 1 theorem, 16 equations, 8 figures, 2 tables, 2 algorithms)

This paper contains 42 sections, 1 theorem, 16 equations, 8 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Single-Cell Atlas Construction via Posterior Sampling
  3. Method
  4. Evaluation on synthetic data
  5. Evaluation on single-cell data
  6. Analysis of the CITE-seq dataset
  7. Analysis of Human Fetal Brain Development Datasets
  8. Discussion
  9. Reproducibility statement
  10. Use of Large Language Models (LLMs)
  11. Acknowledgments
  12. Diffusion Training
  13. Proof of Proposition \ref{['prop:closed-form']}
  14. Model Architecture and Implementation Details for training the Diffusion models used in the single cell experiments
  15. Overview
  16. ...and 27 more sections

Key Result

Proposition 3.1

Assume $f$ is the standard multivariate Gaussian density in $d$ dimensions. Following Gaussian conjugacy, for all $s=0,\ldots,T-1$, the likelihood update step (Line line:likelihood) admits the following update:

Figures (8)

  • Figure 1: UMAP visualizations of the 400 test cells for each of the four configurations. Top row: PCA projections; bottom row: DICE-denoised embeddings. Columns (left to right) correspond to Setups 1–4. Throughout, we refer to the mixture component centered at $1_{15}$ with scale $1.3\,I_{15}$ as Cluster 1, and to the complementary component as Cluster 2 (Gaussian $\mathcal{N}_{15}(0_{15},\,1.5\,I_{15})$ where applicable; heavy-tailed $\mathtt{t}_{\nu=4}(1.3\,I_{15})$ in the latent–prior–shift configuration). Points are colored blue for Cluster 1 and orange for Cluster 2.
  • Figure 1: Average silhouette scores (higher is better) for two methods across four settings.
  • Figure 2: UMAP visualizations of 500 runs of DICE on the same input point in Setup 1 and $\rho = 0.1$. Training data are shown in grey. Left: center of Cluster 2; Right: midpoint between Clusters 1 and 2.
  • Figure 3: UMAP of 1,000 held-out PBMCs from the CITE-seq dataset. Left: PCA embeddings in a 25-dimensional latent space using $\widehat{V}$ from the training set. Right: embeddings after denoising with DICE using a diffusion model trained on the other 9,000 cells.
  • Figure 4: UMAP of 1,000 randomly sampled cells from the Polioudakis2019NeocortexAtlas dataset. Left: PCA embeddings in a 15-dimensional latent space using $\widehat{V}$ from the training set. Right: embeddings after denoising with DICE using a diffusion model trained on the Nowakowski2017CortexTrajectories dataset.
  • ...and 3 more figures

Theorems & Definitions (2)

  • Proposition 3.1
  • Remark 3.2