# LapDDPM: A Conditional Graph Diffusion Model for scRNA-seq Generation with Spectral Adversarial Perturbations

arXiv: https://arxiv.org/abs/2506.13344 · HTML: https://mlsanity.com/paper/2506.13344/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 13 of its 45 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 13 of 13)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Adversarial Attacks on Neural Networks for Graph Data](https://mlsanity.com/paper/1805.07984/) (2018)
- [Adversarial Attack on Graph Structured Data](https://mlsanity.com/paper/1806.02371/) (2018)
- [Hiding Individuals and Communities in a Social Network](https://mlsanity.com/paper/1608.00375/) (2016)
- [A Restricted Black-box Adversarial Framework Towards Attacking Graph Embedding Models](https://mlsanity.com/paper/1908.01297/) (2019)
- [Spectral Augmentations for Graph Contrastive Learning](https://mlsanity.com/paper/2302.02909/) (2023)

## Abstract (arXiv)

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.