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

arXiv:2506.13344v2 Announce Type: replace 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.

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.

LapDDPM is a novel conditional graph diffusion model for scRNA-seq generation. Leveraging spectral adversarial perturbations, it ensures robustness and yields high-fidelity, biologically plausible, and cell-type-specific samples for complex data. Proceedings of Machine Learning Research 333:1 17, 2026 Conference on Health, Inference, and Learning (CHIL) 2026, Seattle, WA

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Biomolecules (q-bio.BM); Cell Behavior (q-bio.CB); Genomics (q-bio.GN)

arXiv:2506.13344 [cs.LG]

(or arXiv:2506.13344v2 [cs.LG] for this version)

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

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