LapDDPM: Spectral Perturbation Diffusion for Robust Single-Cell Manifold Generation

Lorenzo Bini, Stephane Marchand-Maillet
Proceedings of the 7th Conference on Health, Inference, and Learning, PMLR 333:312-328, 2026.

Abstract

Generating high-fidelity and biologically plausible synthetic single-cell RNA sequencing (scRNA-seq) data is a critical challenge in computational biology, driven by the need to model high-dimensional, sparse, and non-linear cellular manifolds. Existing generative models often fail to capture the complex topology of cellular differentiation or lack robustness against technical noise and structural variability. We introduce LapDDPM, a novel conditional Graph Diffusion Probabilistic Model designed for robust manifold learning and high-fidelity generation. LapDDPM integrates graph-based inductive biases with score-based generative modeling, enhanced by a novel spectral adversarial perturbation mechanism. By systematically perturbing graph edge weights along principal spectral modes during training, our method acts as a Distributionally Robust Optimization (DRO) framework, enforcing invariance to structural noise. We further extend LapDDPM to spatial transcriptomics and multi-modal data, treating generation as a robust inverse problem on cellular graphs. Extensive experiments on diverse datasets, including PBMC3K, Dentate Gyrus, HLCA, Visium, and 10x Multiome, demonstrate that LapDDPM significantly outperforms state-of-the-art baselines in distribution matching, manifold preservation, and downstream utility, generating biologically coherent cell states.

Cite this Paper

BibTeX
@InProceedings{pmlr-v333-bini26a, title = {LapDDPM: Spectral Perturbation Diffusion for Robust Single-Cell Manifold Generation}, author = {Bini, Lorenzo and Marchand-Maillet, Stephane}, booktitle = {Proceedings of the 7th Conference on Health, Inference, and Learning}, pages = {312--328}, year = {2026}, editor = {Healey, Elizabeth and Fries, Jason and Pollard, Tom and Tang, Shengpu and Zink, Anna and Hartvigsen, Tom and Agrawal, Monica and Finlayson, Sam and Glicksberg, Benjamin and Beaulieu-Jones, Brett and Wang, Kai and Fontalvo, Daseyra and Sarker, Tasmie and Chen, Irene and Alsentzer, Emily}, volume = {333}, series = {Proceedings of Machine Learning Research}, month = {29--30 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v333/main/assets/bini26a/bini26a.pdf}, url = {https://proceedings.mlr.press/v333/bini26a.html}, abstract = {Generating high-fidelity and biologically plausible synthetic single-cell RNA sequencing (scRNA-seq) data is a critical challenge in computational biology, driven by the need to model high-dimensional, sparse, and non-linear cellular manifolds. Existing generative models often fail to capture the complex topology of cellular differentiation or lack robustness against technical noise and structural variability. We introduce LapDDPM, a novel conditional Graph Diffusion Probabilistic Model designed for robust manifold learning and high-fidelity generation. LapDDPM integrates graph-based inductive biases with score-based generative modeling, enhanced by a novel spectral adversarial perturbation mechanism. By systematically perturbing graph edge weights along principal spectral modes during training, our method acts as a Distributionally Robust Optimization (DRO) framework, enforcing invariance to structural noise. We further extend LapDDPM to spatial transcriptomics and multi-modal data, treating generation as a robust inverse problem on cellular graphs. Extensive experiments on diverse datasets, including PBMC3K, Dentate Gyrus, HLCA, Visium, and 10x Multiome, demonstrate that LapDDPM significantly outperforms state-of-the-art baselines in distribution matching, manifold preservation, and downstream utility, generating biologically coherent cell states.} }
Endnote
%0 Conference Paper %T LapDDPM: Spectral Perturbation Diffusion for Robust Single-Cell Manifold Generation %A Lorenzo Bini %A Stephane Marchand-Maillet %B Proceedings of the 7th Conference on Health, Inference, and Learning %C Proceedings of Machine Learning Research %D 2026 %E Elizabeth Healey %E Jason Fries %E Tom Pollard %E Shengpu Tang %E Anna Zink %E Tom Hartvigsen %E Monica Agrawal %E Sam Finlayson %E Benjamin Glicksberg %E Brett Beaulieu-Jones %E Kai Wang %E Daseyra Fontalvo %E Tasmie Sarker %E Irene Chen %E Emily Alsentzer %F pmlr-v333-bini26a %I PMLR %P 312--328 %U https://proceedings.mlr.press/v333/bini26a.html %V 333 %X Generating high-fidelity and biologically plausible synthetic single-cell RNA sequencing (scRNA-seq) data is a critical challenge in computational biology, driven by the need to model high-dimensional, sparse, and non-linear cellular manifolds. Existing generative models often fail to capture the complex topology of cellular differentiation or lack robustness against technical noise and structural variability. We introduce LapDDPM, a novel conditional Graph Diffusion Probabilistic Model designed for robust manifold learning and high-fidelity generation. LapDDPM integrates graph-based inductive biases with score-based generative modeling, enhanced by a novel spectral adversarial perturbation mechanism. By systematically perturbing graph edge weights along principal spectral modes during training, our method acts as a Distributionally Robust Optimization (DRO) framework, enforcing invariance to structural noise. We further extend LapDDPM to spatial transcriptomics and multi-modal data, treating generation as a robust inverse problem on cellular graphs. Extensive experiments on diverse datasets, including PBMC3K, Dentate Gyrus, HLCA, Visium, and 10x Multiome, demonstrate that LapDDPM significantly outperforms state-of-the-art baselines in distribution matching, manifold preservation, and downstream utility, generating biologically coherent cell states.
APA
Bini, L. & Marchand-Maillet, S.. (2026). LapDDPM: Spectral Perturbation Diffusion for Robust Single-Cell Manifold Generation. Proceedings of the 7th Conference on Health, Inference, and Learning, in Proceedings of Machine Learning Research 333:312-328 Available from https://proceedings.mlr.press/v333/bini26a.html.

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