# Control-Anchored Residual Flow Matching Conditioned on Gene Geometry for Virtual Cell Perturbation Modeling

arXiv: https://arxiv.org/abs/2608.06824 · HTML: https://mlsanity.com/paper/2608.06824/

## 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 6 of its 21 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## 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, 6 of 6)

- [scDFM: Distributional Flow Matching Model for Robust Single-Cell Perturbation Prediction](https://mlsanity.com/paper/2602.07103/) (2026)
- [PerturbDiff: Functional Diffusion for Single-Cell Perturbation Modeling](https://mlsanity.com/paper/2602.19685/) (2026)
- [What Makes a Representation Good for Single-Cell Perturbation Prediction?](https://mlsanity.com/paper/2605.19343/) (2026)
- [Departures: Distributional Transport for Single-Cell Perturbation Prediction with Neural Schr"odinger Bridges](https://mlsanity.com/paper/2511.13124/) (2025)
- [Beyond Independent Genes: Learning Module-Inductive Representations for Single-Cell Gene Perturbation Prediction](https://mlsanity.com/paper/2602.04901/) (2026)
- [Learning Adaptive Perturbation-Conditioned Contexts for Robust Transcriptional Response Prediction](https://mlsanity.com/paper/2602.18885/) (2026)

## Abstract (arXiv)

A central task in virtual cell modeling is predicting single-cell transcriptional responses to unseen genetic perturbations and drug combinations, and biological networks provide valuable priors on gene relationships. Existing graph-based models commonly use the same network to structure gene representations and mediate intergene interactions, thereby implicitly treating stable associations as perturbation-response pathways. Gene Ontology and control-derived coexpression networks encode relatively stable relationships rather than intervention-specific response directions or magnitudes. We therefore propose GeneGeoFlow, which conditions a control-anchored residual flow on gene-wise geometry derived from biological networks to learn intervention-specific transcriptional responses. GeneGeoFlow derives multi-scale spectral coordinates from Gene Ontology and control-derived coexpression networks. A perturbation-conditioned, gene-wise gating module selects relevant structural scales and network sources, yielding intervention-specific gene geometry. The resulting geometry conditions a control-anchored residual flow without explicitly propagating target-derived signals along the graph. Condition-wise optimal transport couples unpaired control and perturbed populations for training, while a Delta-correlation objective aligns the predicted and observed condition-level expression-shift directions. GeneGeoFlow achieves Pearson Delta scores of 0.8979 on the Norman additive benchmark and 0.9088 on five held-out drug combinations in the fixed ComboSciPlex test split. These results support perturbation-conditioned gene geometry as an effective structural prior for intervention-specific response prediction, without conflating stable gene relationships with response propagation.