Generalizable single-cell perturbation response prediction using energy-guided flow matching

Jianan Wei; Jiajun Hong; Guikun Chen; Ning Yang; Lifeng Fan; Wenguan Wang

q-bio.GNSep 27, 2026

Generalizable single-cell perturbation response prediction using energy-guided flow matching

Authors: Jianan Wei, Jiajun Hong, Guikun Chen, Ning Yang, Lifeng Fan, Wenguan Wang

Organizations: Zhejiang University, Hangzhou, Zhejiang, China · Beijing Institute for General Artificial Intelligence, Beijing, China · Peking University Chengdu Academy for Advanced Interdisciplinary Biotechnologies, Chengdu, Sichuan, China

Abstract

Predicting phenotypic and transcriptional responses to perturbations at single-cell resolution provides a powerful tool for probing biological systems. However, existing methods typically rely on fixed mappings learned during training, making it challenging to calibrate distribution shifts or adapt to novel perturbation conditions during inference. Here, we present scEGFlow, an energy-guided flow matching framework that dynamically bridges control and perturbed cellular states. scEGFlow models continuous transitions from control cell populations to perturbed states using conditional flow matching. It then applies condition-specific energy gradients to correct and steer these predictions, enabling flexible adjustments without retraining the flow model. Evaluations across benchmarks spanning imaging phenotypes and transcriptomic profiles show that scEGFlow outperforms existing methods in reconstructing response distributions under both seen and unseen perturbation conditions, faithfully preserving cellular manifold geometry and population heterogeneity. This advantage is notable when adapting to new conditions with only a few measured cells, consistently improving prediction accuracy. Furthermore, scEGFlow accurately recapitulates perturbation-induced up- and down-regulation patterns across consensus gene expression signatures, where energy guidance improves the agreement between predicted and observed regulatory directions. Ultimately, these findings demonstrate that scEGFlow provides a modular, generalizable, and steerable solution for single-cell perturbation modeling. By grounding generative flows in learned biological landscapes, this architecture establishes a new computational paradigm for navigating and manipulating cellular behavior in silico.

Figures & tables

Figure 1: Overview of scEGFlow. (a) Optimal transport establishes soft correspondences between unpaired control and perturbed cells through the transport matrix $T^{*}$ , yielding soft pseudo-pairs for training. (b) The perturbation vector $\bm{p}$ and biological context $\bm{c}$ are encoded as conditional inputs to the flow model, which predicts the velocity field $v_{\theta}(\bm{x}_{t},t,\bm{\xi})$ from the cell state $\bm{x}_{t}$ and time $t$ . (c) During inference, cells are progressively transported toward the perturbed distribution by alternating flow-based velocity updates with energy-guided refinement. The former follows the learned conditional velocity field, whereas the latter adjusts cellular states along the energy gradient toward condition-consistent low-energy regions.

Figure 2: Reconstruction of single-cell perturbation responses across diverse data modalities. (a) Marginal distributions of normalized pERK, Sox9, and pAKT marker intensities on the 4i [ 11 ] benchmark. Measured treated cells are shown in dark blue, and predictions from scEGFlow, scDFM, and PRNet are shown in red, gray, and light blue, respectively. (b–e) IID reconstruction performance on the 4i benchmark, evaluated using MMD 2 (b) , Sinkhorn divergence (c) , Pearson correlation between condition-level mean profiles (d) , and energy distance (e) . Lower values are better for MMD 2 , Sinkhorn divergence, and energy distance, whereas higher values are better for Pearson correlation. (f) Drug-level comparison between scEGFlow and the MeanExp baseline for six selected 4i perturbations. The horizontal axis shows the log 2 ratio of the energy distances obtained by MeanExp and scEGFlow. (g) UMAP visualization of predicted and measured 4i cells aggregated across all evaluated drug treatments in a shared phenotypic state space. Cells are colored by normalized mean pERK intensity. AU, arbitrary units. (h) UMAP comparison of SciPlex3 [ 3 ] IID response reconstruction across aggregated drug-dose conditions. Measured target cells are shown in gray and predicted cells from each method are shown in blue.

Method	4i				SciPlex3
Method	Energy $\downarrow$	Sinkhorn $\downarrow$	MMD 2 $\downarrow$	Pearson $\uparrow$	Energy $\downarrow$	Sinkhorn $\downarrow$	MMD 2 $\downarrow$	Pearson $\uparrow$
MeanExp	0.0510	1.4463	0.4839	0.9925	2.2626	12.7494	0.6887	0.9914
CellOT [ 11 ]	3.1399	2.0230	0.0199	0.5513	–	–	–	–
biolord [ 22 ]	0.1507	1.2904	0.2411	0.9669	1.1494	0.9318	0.2192	0.9949
CPA [ 6 ]	0.6125	0.3091	0.0257	0.7455	2.9388	1.5674	0.2509	0.9476
PRNet [ 1 ]	0.0208	0.0254	0.0145	0.9910	0.6419	0.3788	0.0145	0.9856

Table 1: IID perturbation prediction on 4i [ 11 ] and SciPlex3 [ 3 ] .

Method	OOD drug-dose				OOD cellular context
Method	Energy $\downarrow$	Sinkhorn $\downarrow$	MMD 2 $\downarrow$	Pearson $\uparrow$	Energy $\downarrow$	Sinkhorn $\downarrow$	MMD 2 $\downarrow$	Pearson $\uparrow$
MeanExp	0.8735	5.7422	0.6824	0.9966	52.9832	27.5550	0.7647	0.8090
biolord [ 22 ]	0.7792	0.5939	0.2114	0.9966	51.4051	26.7684	0.7584	0.8154
CPA [ 6 ]	2.2859	1.2211	0.2385	0.9607	14.9031	7.5212	0.4386	0.6901
PRNet [ 1 ]	0.4077	0.2211	0.0051	0.9909	55.4931	22.1669	0.1777	0.8003
CellFlow [ 12 ]	0.5218	0.3692	0.0065	0.9977	22.3046	12.2336	0.1624	0.9254

Table 2: OOD perturbation prediction under unseen drug-dose conditions and in an unseen cellular context on SciPlex3 [ 3 ] .

Figure 3: Generalization of single-cell perturbation responses across unseen chemical and cellular contexts. (a) UMAP visualization of unperturbed cells colored by three cell types (A549, K562, and MCF7 cells). (b) UMAP visualization of measured MCF7 cells treated with 20 representative compounds at the highest profiled dose. (c) Distribution-level prediction performance for held-out SciPlex3 [ 3 ] drug-dose conditions. Boxplots compare the energy distance and MMD 2 between predicted and measured target-cell populations over the OOD test set. (d) Gene-expression distributions of the five most strongly perturbed genes for three held-out drug-dose conditions, comparing control, measured perturbed, and scEGFlow-predicted cells. (e) Covariance matrices over the first 10 principal components for the held-out Mesna_0.1 condition, comparing the measured target population with populations predicted by scEGFlow and the baseline methods; all six matrices are computed in the same PCA basis fitted on the training cells. (f) Heatmap of the measured treated-versus-control response magnitude across representative drug-dose conditions in three cell types. Response magnitude is computed as the root-mean-square of the gene-wise treated-minus-control mean expression shifts after z-score standardization over the retained genes. (g) Gene-wise MMD 2 for scEGFlow and CellFlow on the most strongly perturbed genes, selected by the absolute treated-minus-control mean shift in the held-out A549 context. For each gene, cells across all evaluated drug-dose conditions are pooled before computing MMD 2 between measured and predicted expression distributions. Lower values indicate better agreement.

Method	Energy $\downarrow$	Sinkhorn $\downarrow$	MMD 2 $\downarrow$	Pearson $\uparrow$
CellOT [ 11 ]	28.19	112.71	0.0262	0.9625
biolord [ 22 ]	37.98	98.97	0.6087	0.9522
CPA [ 6 ]	29.09	94.05	0.3239	0.9608
PRNet [ 1 ]	50.59	202.66	0.0259	0.9337
CellFlow [ 12 ]	25.06	93.52	0.0664	0.9692
scDFM [ 21 ]	91.23	246.80	0.0354	0.8848

Table 3: OOD perturbation prediction on ComboSciPlex [ 6 ] .

Figure 4: Generalization to unseen drug combinations and sample-efficient prediction. (a) UMAP visualization of measured ComboSciPlex [ 6 ] cells, showing the five held-out drug-combination responses and their positions relative to the response manifold. (b) Predicted versus measured mean gene expression for the five held-out drug combinations, shown for all genes and the top 50 differentially expressed genes (DEGs). (c) Expression distributions of the top two DEGs for each held-out drug combination, comparing control, measured treated, and scEGFlow-predicted cells. (d) Few-shot prediction on the 4i [ 11 ] benchmark under different numbers of target-condition training cells, evaluated using Pearson correlation, MMD 2 , Sinkhorn divergence, and energy distance. (e) UMAP comparison of zero-shot predictions, 3-shot predictions, 5-shot predictions and measured target cells, colored by normalized pERK intensity.

Figure 5: Directional concordance with L1000 [ 20 ] perturbational signatures. (a) Mean directional concordance between predicted perturbation responses and the corresponding L1000 Level 5 consensus signatures. (b) Context-level distribution of directional concordance across all $111$ evaluation contexts. Each point represents one specific cell line-drug-dose condition.

Dataset	Cells/profiles	Features	Contexts	Conditions	Readout
4i [ 11 ]	77,743	48	1	27	imaging phenotype
SciPlex3 [ 3 ]	290,888	2,000	3	749	scRNA-seq
ComboSciPlex [ 6 ]	63,378	2,000	1	32	scRNA-seq
L1000 Level 3 [ 20 ]	24,104	978	21	110	gene-expression profiles

Table S1: Overview of the datasets used in this study.

Dataset	Feature dim.	Training steps	Batch size	Learning rate
4i [ 11 ]	48	100,000	256	$10^{-6}$
SciPlex3 [ 3 ]	200	50,000	256	$10^{-7}$
ComboSciPlex [ 6 ]	200	50,000	256	$10^{-7}$
LINCS L1000 [ 20 ]	768	30,000	128	$10^{-7}$

Table S2: Training hyperparameters for the conditional flow-matching model.

Dataset	Feature dim.	Training steps	Batch size	Learning rate	Weight decay
4i [ 11 ]	48	5,000	256	$10^{-4}$	$10^{-4}$
SciPlex3 [ 3 ]	200	300	256	$10^{-4}$	$10^{-4}$
ComboSciPlex [ 6 ]	200	5,000	256	$10^{-4}$	$10^{-4}$
LINCS L1000 [ 20 ]	768	300	128	$10^{-4}$	$10^{-4}$

Table S3: Training hyperparameters for the energy model.

Condition	Model	Energy $\downarrow$	Sinkhorn $\downarrow$	MMD 2 $\downarrow$	Pearson $\uparrow$
ENMD-2076_0.1	w/o energy guidance	0.2380	0.1360	0.0040	0.9947
ENMD-2076_0.1	w/ energy guidance	0.2050	0.1180	0.0035	0.9955
WP1066_0.01	w/o energy guidance	0.2520	0.1450	0.0041	0.9942
WP1066_0.01	w/ energy guidance	0.2180	0.1260	0.0036	0.9951
Mesna_0.1	w/o energy guidance	0.3530	0.2035	0.0054	0.9907
Mesna_0.1	w/ energy guidance	0.3084	0.1733	0.0046	0.9929

Table S4: Prediction performance with and without energy guidance on three held-out OOD drug-dose conditions in SciPlex3 [ 3 ] . Both settings share the same trained flow model.

Condition	Model	Energy $\downarrow$	Sinkhorn $\downarrow$	MMD 2 $\downarrow$	Pearson $\uparrow$
Dacinostat + Danusertib	w/o energy guidance	25.8631	100.5147	0.0656	0.9588
Dacinostat + Danusertib	w/ energy guidance	21.7346	83.7241	0.0476	0.9720
Givinostat + Cediranib	w/o energy guidance	29.4728	112.7362	0.0498	0.9792
Givinostat + Cediranib	w/ energy guidance	24.1183	91.5836	0.0524	0.9760
Panobinostat + Alvespimycin	w/o energy guidance	64.7315	195.6841	0.1215	0.7904
Panobinostat + Alvespimycin	w/ energy guidance	55.8427	168.9142	0.0987	0.8210

Table S5: Prediction performance with and without energy guidance on five held-out ComboSciPlex [ 6 ] OOD drug combinations. Both settings share the same trained flow model. Average rows are obtained by pooling all test cells from the five held-out combinations and recomputing each metric on the pooled measured and predicted populations.

$\lambda$	Energy $\downarrow$	Sinkhorn $\downarrow$	MMD 2 $\downarrow$	Pearson $\uparrow$
0.0000	0.2810	0.1615	0.0045	0.9932
0.0125	0.2705	0.1554	0.0043	0.9936
0.0250	0.2588	0.1480	0.0041	0.9940
0.0500	0.2438	0.1391	0.0039	0.9945
0.1000	0.2479	0.1415	0.0040	0.9944
0.2000	0.2676	0.1532	0.0043	0.9937

Table S6: Sensitivity of SciPlex3 [ 3 ] OOD drug-dose prediction to the guidance coefficient

\lambda

$\lambda$	Energy $\downarrow$	Sinkhorn $\downarrow$	MMD 2 $\downarrow$	Pearson $\uparrow$
0.0000	29.9767	111.6462	0.0618	0.9597
0.0125	28.4163	105.7328	0.0589	0.9621
0.0250	26.6835	99.2846	0.0554	0.9646
0.0500	24.8578	93.0152	0.0527	0.9667
0.1000	25.1936	94.2671	0.0532	0.9662
0.2000	27.1849	101.4385	0.0569	0.9637

Table S7: Sensitivity of ComboSciPlex [ 6 ] OOD drug combination prediction to the guidance coefficient

\lambda

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Synergy-Aware Residual Flow Matching for Single-Cell Perturbation Prediction

Jingrui Wu, Wangyun Dan

Department of Statistics, Rice University, Houston, TX, USA · Department of Biostatistics and Bioinformatics, Emory University, Atlanta, GA, USA

Single-Cell Perturbation Modeling Flow-Based Generative Modeling Residual Learning

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Predicting single-cell responses to genetic and chemical perturbations is important for understanding regulatory mechanisms and prioritizing therapeutic interventions. Existing methods have made progress by modeling perturbation-conditioned expression shifts with neural networks, graph priors, foundation-model representations, or distributional generative models. However, combinatorial perturbation prediction remains challenging because much of the response can be explained by additive single-perturbation effects, while the biologically informative signal often lies in a smaller non-additive residual induced by perturbation interactions. Directly generating the full post-perturbation expression profile may therefore allocate substantial capacity to the dominant additive component and underemphasize synergy-specific structure. To address this issue, we propose SynGeneFlow, a synergy-aware flow matching framework that anchors the source distribution at an additive prior and learns a residual flow toward the true perturbed state. SynGeneFlow further incorporates perturbation-conditioned gene interaction modeling, where a static gene-gene mask provides biological structure and a perturbation-dependent deformation bias dynamically modulates gene-gene coupling. To preserve population-level response structure, we align both endpoint distributions and biological residual distributions with MMD-based regularization. We evaluate SynGeneFlow on genetic and drug perturbation benchmarks under observed-single, held-out, and cross-modality settings. The results demonstrate that residualizing flow matching around additive perturbation effects provides a biologically grounded and robust framework for single-cell perturbation response prediction.

Abstract

Single-Cell Perturbation Modeling

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