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Squidiff: predicting cellular development and responses to perturbations using a diffusion model

Nature Methods volume 23, pages 65–77 (2026)Cite this article

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Abstract

Single-cell sequencing has revolutionized our understanding of cellular heterogeneity and responses to environmental stimuli. However, mapping transcriptomic changes across diverse cell types in response to various stimuli and elucidating underlying disease mechanisms remains challenging. Here we present Squidiff, a diffusion model-based generative framework that predicts transcriptomic changes across diverse cell types in response to environmental changes. We demonstrate the robustness of Squidiff across cell differentiation, gene perturbation and drug response prediction. Through continuous denoising and semantic feature integration, Squidiff learns transient cell states and predicts high-resolution transcriptomic landscapes over time and conditions. Furthermore, we applied Squidiff to model blood vessel organoid development and cellular responses to neutron irradiation and growth factors. Our results demonstrate that Squidiff enables in silico screening of molecular landscapes and cellular state transitions, facilitating rapid hypothesis generation and providing valuable insights into the regulatory principles of cell fate decisions.

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Fig. 1: Overview of Squidiff and its performance on synthetic data.
Fig. 2: Squidiff predicts cell differentiation.
Fig. 3: Squidiff predicts gene and drug perturbation.
Fig. 4: Squidiff predicts cell differentiation processes in BVOs.
Fig. 5: Structural damage and metabolic phenotype alteration in BVOs induced by neutron irradiation.
Fig. 6: Treatment potential of G-CSF in securing against radiation disruption in BVOs.

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Data availability

The public dataset of scRNA-seq of iPSCs differentiating toward endoderm27 was downloaded from Zenodo (https://zenodo.org/records/3625024#.Xil-0y2cZ0s)66. The dataset for nonadditive gene perturbation34 was downloaded from GSE133344. The dataset for drug treatment of melanoma cells8 was downloaded from https://www.research-collection.ethz.ch/handle/20.500.11850/609681. The public dataset of drug screening in glioblastoma35 was downloaded from accession GSE148842. The sci-Plex3 dataset37 was downloaded from GSM4150378. The raw single-cell sequencing data of BVOs are available on figshare (https://doi.org/10.6084/m9.figshare.27948633)67. Source data are provided with this paper.

Code availability

The Squidiff package and code to reproduce the results in this study are available on the GitHub repositories: https://github.com/siyuh/Squidiff and https://github.com/siyuh/Squidiff_reproducibility. The code is also deposited at Zenodo (https://doi.org/10.5281/zenodo.15061773)65.

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Acknowledgements

We thank S. Quake and K. Preechakul for insightful discussions on virtual cells and the diffusion model; and S. Wang, J. H. Lee and R.B.-L. Berris for their assistance with scRNA-seq analysis and cell culture. We also appreciate the staff at Columbia’s Center for Radiological Research for their support in operating ionizing radiation equipment. This study used resources from the Herbert Irving Comprehensive Cancer Center Confocal, Specialized Microscopy Shared Resource and the Genomics and High Throughput Screening Shared Resource, partially funded by NIH/NCI Cancer Center Support Grant P30CA013696. The Columbia IND Neutron Facility was developed under NIAID grant U19 AI067773. We gratefully acknowledge funding support from the Translational Research Institute for Space Health (TRISH/NASA) (RAD0104 and NNX16A069A to G.V.-N. and K.W.L.).

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Author notes

  1. These authors contributed equally: Siyu He, Yuefei Zhu, Daniel Naveed Tavakol.

Authors and Affiliations

  1. Department of Biomedical Engineering, Columbia University, New York, NY, USA

    Siyu He, Yuefei Zhu, Daniel Naveed Tavakol, Yeh-Hsing Lao, Zixian Zhu, Cong Xu, Raju Tomer, Gordana Vunjak-Novakovic, Elham Azizi & Kam W. Leong

  2. Irving Institute for Cancer Dynamics, Columbia University, New York, NY, USA

    Siyu He & Elham Azizi

  3. Department of Biomedical Data Science, Stanford University, Stanford, CA, USA

    Siyu He & James Zou

  4. Department of Computer Sciences, Stanford University, Stanford, CA, USA

    Haotian Ye & James Zou

  5. Department of Pharmaceutical Sciences, University at Buffalo, Buffalo, NY, USA

    Yeh-Hsing Lao

  6. Department of Biological Sciences, Columbia University, New York, NY, USA

    Shradha Chauhan & Raju Tomer

  7. Center for Radiological Research, Columbia University, New York, NY, USA

    Guy Garty

  8. Herbert Irving Comprehensive Cancer Center, Columbia University, New York, NY, USA

    Gordana Vunjak-Novakovic & Elham Azizi

  9. Department of Electrical Engineering, Stanford University, Stanford, CA, USA

    James Zou

  10. Department of Computer Sciences, Columbia University, New York, NY, USA

    Elham Azizi

  11. Data Science Institute, Columbia University, New York, NY, USA

    Elham Azizi

  12. Department of Systems Biology, Columbia University Irving Medical Center, New York, NY, USA

    Kam W. Leong

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Contributions

K.W.L., E.A. and J.Z. conceived the study and provided overall supervision of the study. S.H., Y.Z. and D.N.T. designed the BVO study and performed experiments. S.H. and H.Y. designed and developed the model. S.H., Y.Z., D.N.T., H.Y., Z.Z., C.X. and S.C. analyzed and interpreted data. G.G. performed irradiation experiments. R.T. and G.V.-N. provided additional supervision. S.H., Y.Z., D.N.T., H.Y., J.Z., E.A. and K.W.L. wrote the paper. All authors reviewed, contributed to and approved the paper.

Corresponding authors

Correspondence to James Zou, Elham Azizi or Kam W. Leong.

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Nature Methods thanks Sudin Bhattacharya, Qing Nie and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reportsare available. Primary Handling Editor: Madhura Mukhopadhyay, in collaboration with the Nature Methods team.

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Multichannel confocal imaging for BVOs.

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He, S., Zhu, Y., Tavakol, D.N. et al. Squidiff: predicting cellular development and responses to perturbations using a diffusion model. Nat Methods 23, 65–77 (2026). https://doi.org/10.1038/s41592-025-02877-y

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