# Towards generalizable single-cell perturbation modeling via the Conditional Monge Gap

arXiv: https://arxiv.org/abs/2504.08328 · HTML: https://mlsanity.com/paper/2504.08328/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 59 references that are in the map.
- First posted on arXiv 11 Apr 2025.

## Builds on (most cited first, 24 of 24)

- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Analyzing Learned Molecular Representations for Property Prediction](https://mlsanity.com/paper/1904.01561/) (2019)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [Improving GANs Using Optimal Transport](https://mlsanity.com/paper/1803.05573/) (2018)
- [Optimal Transport Tools (OTT): A JAX Toolbox for all things Wasserstein](https://mlsanity.com/paper/2201.12324/) (2022)
- [Supervised Training of Conditional Monge Maps](https://mlsanity.com/paper/2206.14262/) (2022)
- [Predicting Cellular Responses to Novel Drug Perturbations at a Single-Cell Resolution](https://mlsanity.com/paper/2204.13545/) (2022)
- [Unbalancedness in Neural Monge Maps Improves Unpaired Domain Translation](https://mlsanity.com/paper/2311.15100/) (2023)
- [The Monge Gap: A Regularizer to Learn All Transport Maps](https://mlsanity.com/paper/2302.04953/) (2023)
- [GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomics](https://mlsanity.com/paper/2310.09254/) (2023)
- [Neural Unbalanced Optimal Transport via Cycle-Consistent Semi-Couplings](https://mlsanity.com/paper/2209.15621/) (2022)
- [Fast Nonlinear Vector Quantile Regression](https://mlsanity.com/paper/2205.14977/) (2022)
- [Fast and scalable Wasserstein-1 neural optimal transport solver for single-cell perturbation prediction](https://mlsanity.com/paper/2411.00614/) (2024)
- [Vector Quantile Regression on Manifolds](https://mlsanity.com/paper/2307.01037/) (2023)
- [Quantum Theory and Application of Contextual Optimal Transport](https://mlsanity.com/paper/2402.14991/) (2024)
- [Efficient Fine-Tuning of Single-Cell Foundation Models Enables Zero-Shot Molecular Perturbation Prediction](https://mlsanity.com/paper/2412.13478/) (2024)
- [Learning Cross-Domain Representations for Transferable Drug Perturbations on Single-Cell Transcriptional Responses](https://mlsanity.com/paper/2412.19228/) (2024)

## Built on by (most cited first, 3 of 3)

- [Branched Schr"odinger Bridge Matching](https://mlsanity.com/paper/2506.09007/) (2025)
- [STRAND: Sequence-Conditioned Transport for Single-Cell Perturbations](https://mlsanity.com/paper/2602.10156/) (2026)
- [PerturbMap: Cross-Context Transfer of Single-Cell Perturbation Responses](https://mlsanity.com/paper/2607.28090/) (2026)

## Abstract (arXiv)

Learning the response of single-cells to various treatments offers great potential to enable targeted therapies. In this context, neural optimal transport (OT) has emerged as a principled methodological framework because it inherently accommodates the challenges of unpaired data induced by cell destruction during data acquisition. However, most existing OT approaches are incapable of conditioning on different treatment contexts (e.g., time, drug treatment, drug dosage, or cell type) and we still lack methods that unanimously show promising generalization performance to unseen treatments. Here, we propose the Conditional Monge Gap which learns OT maps conditionally on arbitrary covariates. We demonstrate its value in predicting single-cell perturbation responses conditional to one or multiple drugs, a drug dosage, or combinations thereof. We find that our conditional models achieve results comparable and sometimes even superior to the condition-specific state-of-the-art on scRNA-seq as well as multiplexed protein imaging data. Notably, by aggregating data across conditions we perform cross-task learning which unlocks remarkable generalization abilities to unseen drugs or drug dosages, widely outperforming other conditional models in capturing heterogeneity (i.e., higher moments) in the perturbed population. Finally, by scaling to hundreds of conditions and testing on unseen drugs, we narrow the gap between structure-based and effect-based drug representations, suggesting a promising path to the successful prediction of perturbation effects for unseen treatments.