Enforcing Latent Euclidean Geometry in Single-Cell VAEs for Manifold Interpolation

Alessandro Palma, Sergei Rybakov, Leon Hetzel, Stephan Günnemann, Fabian J Theis
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:47478-47508, 2025.

Abstract

Latent space interpolations are a powerful tool for navigating deep generative models in applied settings. An example is single-cell RNA sequencing, where existing methods model cellular state transitions as latent space interpolations with variational autoencoders, often assuming linear shifts and Euclidean geometry. However, unless explicitly enforced, linear interpolations in the latent space may not correspond to geodesic paths on the data manifold, limiting methods that assume Euclidean geometry in the data representations. We introduce FlatVI, a novel training framework that regularises the latent manifold of discrete-likelihood variational autoencoders towards Euclidean geometry, specifically tailored for modelling single-cell count data. By encouraging straight lines in the latent space to approximate geodesic interpolations on the decoded single-cell manifold, FlatVI enhances compatibility with downstream approaches that assume Euclidean latent geometry. Experiments on synthetic data support the theoretical soundness of our approach, while applications to time-resolved single-cell RNA sequencing data demonstrate improved trajectory reconstruction and manifold interpolation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-palma25a, title = {Enforcing Latent {E}uclidean Geometry in Single-Cell {VAE}s for Manifold Interpolation}, author = {Palma, Alessandro and Rybakov, Sergei and Hetzel, Leon and G\"{u}nnemann, Stephan and Theis, Fabian J}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {47478--47508}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/palma25a/palma25a.pdf}, url = {https://proceedings.mlr.press/v267/palma25a.html}, abstract = {Latent space interpolations are a powerful tool for navigating deep generative models in applied settings. An example is single-cell RNA sequencing, where existing methods model cellular state transitions as latent space interpolations with variational autoencoders, often assuming linear shifts and Euclidean geometry. However, unless explicitly enforced, linear interpolations in the latent space may not correspond to geodesic paths on the data manifold, limiting methods that assume Euclidean geometry in the data representations. We introduce FlatVI, a novel training framework that regularises the latent manifold of discrete-likelihood variational autoencoders towards Euclidean geometry, specifically tailored for modelling single-cell count data. By encouraging straight lines in the latent space to approximate geodesic interpolations on the decoded single-cell manifold, FlatVI enhances compatibility with downstream approaches that assume Euclidean latent geometry. Experiments on synthetic data support the theoretical soundness of our approach, while applications to time-resolved single-cell RNA sequencing data demonstrate improved trajectory reconstruction and manifold interpolation.} }
Endnote
%0 Conference Paper %T Enforcing Latent Euclidean Geometry in Single-Cell VAEs for Manifold Interpolation %A Alessandro Palma %A Sergei Rybakov %A Leon Hetzel %A Stephan Günnemann %A Fabian J Theis %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-palma25a %I PMLR %P 47478--47508 %U https://proceedings.mlr.press/v267/palma25a.html %V 267 %X Latent space interpolations are a powerful tool for navigating deep generative models in applied settings. An example is single-cell RNA sequencing, where existing methods model cellular state transitions as latent space interpolations with variational autoencoders, often assuming linear shifts and Euclidean geometry. However, unless explicitly enforced, linear interpolations in the latent space may not correspond to geodesic paths on the data manifold, limiting methods that assume Euclidean geometry in the data representations. We introduce FlatVI, a novel training framework that regularises the latent manifold of discrete-likelihood variational autoencoders towards Euclidean geometry, specifically tailored for modelling single-cell count data. By encouraging straight lines in the latent space to approximate geodesic interpolations on the decoded single-cell manifold, FlatVI enhances compatibility with downstream approaches that assume Euclidean latent geometry. Experiments on synthetic data support the theoretical soundness of our approach, while applications to time-resolved single-cell RNA sequencing data demonstrate improved trajectory reconstruction and manifold interpolation.
APA
Palma, A., Rybakov, S., Hetzel, L., Günnemann, S. & Theis, F.J.. (2025). Enforcing Latent Euclidean Geometry in Single-Cell VAEs for Manifold Interpolation. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:47478-47508 Available from https://proceedings.mlr.press/v267/palma25a.html.

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