Latent Causal Diffusions for Single-Cell Perturbation Modeling

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Video file (mp4)

The gist

The gist: Latent causal diffusion (LCD) is a generative model that frames single-cell gene expression as a stationary diffusion process observed under measurement noise, allowing it to predict

In short

Latent Causal Diffusion (LCD) is a generative model that treats single-cell gene expression as a stationary diffusion process under measurement noise. It predicts unseen perturbation combinations and learns an explicit, gene-level dynamical system of gene regulation. This framework, combined with Causal Linearization via Perturbation Responses (CLIPR), maps underlying causal mechanisms and identifies functional gene modules.

Key concepts

Latent Causal Diffusion (LCD)
LCD frames single-cell gene expression as a stationary stochastic process. It models the evolution of gene states using a stochastic differential equation where the drift function captures causal regulatory mechanisms, allowing inference of these dynamics from observed state distributions without needing time-resolved data.
Stationary Distribution
In LCDs, the SDEs induce a time-independent distribution over gene states. This property is crucial because it enables researchers to infer the underlying causal dynamics (the drift function) directly from the static distribution of gene expression states, simplifying the modeling process.
Causal Linearization via Perturbation Responses (CLIPR)
CLIPR is a method used to interpret the learned dynamics. It approximates direct gene-gene causal effects by analyzing how the system responds to perturbations. It provably recovers causal structure under a linear drift assumption, distinguishing true causal links from simple differential expression.
Gene Modules
By applying hierarchical clustering based on shortest path distances in the CLIPR graph, the model organizes genes into coherent functional modules. These modules are enriched for specific Gene Ontology terms and canonical pathways, revealing tightly connected regulatory groups that standard analysis misses.

Terminology used across episodes

This episode discusses

The paper

Latent Causal Diffusions for Single-Cell Perturbation Modeling · Read on arXiv

Lars Lorcha, Jiaqi Zhangb, Charlotte Bunned, Andreas Krausea, * Bernhard Schölkopff, Jiaqi Zhangb, Charlotte Bunned, Andreas Krausea

Department of Computer Science, ETH Zürich · Laboratory for Information and Decision Systems, Massachusetts Institute of Technology · Eric and Wendy Schmidt Center at the Broad Institute of MIT and Harvard · School of Computer and Communication Sciences, EPFL · Swiss Institute for Experimental Cancer Research at the School of Life Sciences, EPFL · Max Planck Institute for Intelligent Systems Tübingen · ELLIS Institute Tübingen

Perturbation screens hold the potential to systematically map regulatory processes at single-cell resolution, yet modeling and predicting transcriptome-wide responses to perturbations remains a major computational challenge. Existing methods often underperform simple baselines, fail to disentangle measurement noise from biological signal, and provide limited insight into the causal structure governing cellular responses. Here, we present the latent causal diffusion (LCD), a generative model that frames single-cell gene expression as a stationary diffusion process observed under measurement noise. LCD outperforms established approaches in predicting the distributional shifts of unseen perturbation combinations in single-cell RNA-sequencing screens while simultaneously learning a mechanistic dynamical system of gene regulation. To interpret these learned dynamics, we develop an approach we call causal linearization via perturbation responses (CLIPR), which yields an approximation of the direct causal effects between all genes modeled by the diffusion. CLIPR provably identifies causal effects under a linear drift assumption and recovers causal structure in both simulated systems and a genome-wide perturbation screen, where it clusters genes into coherent functional modules and resolves causal relationships that standard differential expression analysis cannot. The LCD-CLIPR framework bridges generative modeling with causal inference to predict unseen perturbation effects and map the underlying regulatory mechanisms of the transcriptome.

DOI: 10.1073/pnas.2602630123

Transcript

Introduction to the show: ident: Genomics Radio. Generated commentary on the latest computational biology and genomics papers.

Ines: I'm Ines, and with me are Marcus and Yuki, guest researcher.

Marcus: Today's paper: "Latent Causal Diffusions for Single-Cell Perturbation Modeling".

Ines: The gist: Latent causal diffusion (LCD) is a generative model that frames single-cell gene expression as a stationary diffusion process observed under measurement noise,

Marcus: First, who's behind it and why it matters.

Paper summary: Marcus: So we’ve covered the basics of the paper called "Latent Causal Diffusions for Single-Cell Perturbation Modeling". To recap, the core idea is framing gene expression as a latent stationary dynamical system observed under measurement noise and using that to predict distributional shifts in perturbation combinations.

Ines: Right. The thesis is that existing methods struggle because they often conflate technical artifacts with biological signals and fail to characterize how perturbations propagate through genetic pathways to drive transcriptional changes, giving limited structural insight into the causal mechanisms governing cellular responses.

Marcus: So, they introduce Latent Causal Diffusion or LCD, which treats gene expression as a latent stationary dynamical system observed under measurement noise. By assuming this diffusion process operates in equilibrium, they can infer the functional causal mechanisms of the SDEs without direct observation of how expression changes over time itself.

Yuki: It’s about using the stationary distribution to infer dynamics rather than tracking time-resolved observations, which is a big conceptual shift for how we think about biological systems.

Ines: They formalize gene regulation as a diffusion process governed by a system of stochastic differential equations, where each gene’s expression evolves mechanistically as a function of its regulators. This allows them to infer the functional causal mechanisms without direct observation of the temporal dynamics, viewing single-cell data as samples from the stationary distribution under a measurement model.

Marcus: The drift function f is parameterized by a neural network that shares parameters across all the causal mechanisms of each gene, and perturbations modify this hidden state via learned embeddings. This works because gene expressions tend to co-vary across perturbations, and they cluster by their shared transcriptomic effects.

Yuki: So the model learns these latent embeddings as it figures out how perturbations affect that hidden state, which is what allows it to capture those shared effects you see in the data.

Ines: And then they develop Causal Linearization via Perturbation Responses, or CLIPR, which is used to interpret those learned causal dependencies in a more direct way by approximating the direct gene-gene causal effects modeled in the diffusion process.

Marcus: CLIPR provably identifies causal effects under a linear drift assumption and recovers the causal structure in both simulated systems and a genome-wide perturbation screen, where it clusters genes into coherent functional modules and resolves causal relationships that standard differential expression analysis just can't see.

Yuki: That could really help us map out biological pathways that are hidden when we only look at which genes are up or down in a specific comparison.

Ines: It’s about using this framework to bridge generative modeling with causal inference to predict unseen perturbation effects and map the underlying regulatory mechanisms of the transcriptome.

Marcus: That’s the big picture here, moving from just seeing correlation to explicitly mapping how one gene causes another within this complex system.

Conclusion: Ines: So, wrapping up this discussion on "Latent Causal Diffusions for Single-Cell Perturbation Modeling", the authors are proposing a generative model that treats single-cell expression as a latent stationary diffusion process observed under measurement noise to predict perturbation effects and learn the underlying regulatory mechanisms.

Marcus: Essentially, the paper shows that by using LCD, they can predict distributional shifts of unseen perturbation combinations more accurately than established approaches while learning an explicit, gene-level dynamical system as the generative model.

Yuki: The main implication seems to be that we are gaining a way to map out regulatory mechanisms that were previously hidden under standard differential expression analysis.

Ines: They’re showing how this framework can infer direct causal effects among genes in Perturb-seq screens by training on a genome-wide Perturb-seq assay, uncovering regulatory mechanisms in K562 cells that remain hidden under standard differential expression analysis.

Marcus: So the title suggests they are creating a model that moves beyond simple correlation to explicitly mapping how one gene causes another within this complex system using their LCD-CLIPR framework.

Yuki: It’s about seeing the underlying structure of regulation, not just the list of differentially expressed genes in a comparison.

Ines: It’s about seeing the underlying structure of regulation, not just the list of differentially expressed genes in a comparison.

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