TempoBridge: Source-Conditioned Flow Matching with Optimal Transport Couplings for Single-Cell Population Transitions

Bowen Han; Lingbei Meng; Shihuan Luo; Yupeng Zang; Wenlin LI; Peize He; Yaodi Luo; Lian Zhang

cs.LGOct 4, 2026

TempoBridge: Source-Conditioned Flow Matching with Optimal Transport Couplings for Single-Cell Population Transitions

Authors: Bowen Han, Lingbei Meng, Shihuan Luo, Yupeng Zang, Wenlin LI, Peize He, Yaodi Luo, Lian Zhang,

Organizations: Universiti Sains Malaysia · The Chinese University of Hong Kong Shenzhen · Shenzhen Loop Area Institute · Shenzhen Research Institute of Big Data ·

Abstract

Destructive single-cell measurements provide unpaired population snapshots rather than observations of the same cells across conditions. Local cell states and transition requests may also be insufficient to distinguish responses across source populations. We introduce TempoBridge, a common source-conditioned transport formulation for temporal, genetic, and chemical population transitions. Source cells initialize latent transport and provide a fixed empirical population summary. The velocity field receives this summary alongside the evolving cell state, flow time, and a structured transition descriptor. Minibatch optimal transport (OT) supplies couplings only for conditional flow-matching training paths; inference requires neither target expression nor OT computation. On held-out donors, TempoBridge achieves an Energy distance of 0.129 versus 0.144 for scGen. Genetic mean-expression $L_2$ error is 2.261 versus 3.156 for scGPT-scratch under Seen 2/2. On held-out compounds, condition-averaged drug-effect correlation is 0.598 versus 0.561 for the CellFlow adapter. Temporal ablations show higher mean distributional error after removing source context, replacing optimal transport with random pairing, or replacing flow matching with static residual regression. Together, these results demonstrate the predictive utility of a common source-conditioned transport formulation across held-out donors, gene combinations, and compounds.

Figures & tables

Figure 1: TempoBridge overview. (a) Temporal, genetic, and drug-response models use a common source-conditioned transport formulation and are trained independently. (b) Source cells initialize latent particles and provide a fixed empirical population summary. The velocity field takes the evolving latent state, flow time, source summary, and encoded transition descriptor as inputs. Each task model has its own expression decoder. Minibatch OT constructs training paths; inference requires no target expression or OT computation.

Method	MMD $\downarrow$	Energy $\downarrow$	$\Delta r\uparrow$	DE@100 $\uparrow$
scGen	$0.4300\pm 0.0072$	$0.1442\pm 0.0019$	$0.6168\pm 0.0049$	$0.5111\pm 0.0043$
Conditional VAE ( 2015 )	$0.4243\pm 0.0023$	$0.1462\pm 0.0006$	$0.5826\pm 0.0011$	$0.4532\pm 0.0053$
Conditional MLP	$0.4302\pm 0.0032$	$0.1507\pm 0.0021$	$0.5742\pm 0.0040$	$0.4448\pm 0.0070$
CellOT	$0.4459\pm 0.0105$	$0.1521\pm 0.0022$	$0.5849\pm 0.0053$	$0.4579\pm 0.0082$
PRESCIENT	$0.4967\pm 0.0052$	$0.1635\pm 0.0035$	$0.6210\pm 0.0064$	$0.5220\pm 0.0035$
scNODE	$0.5628\pm 0.0018$	$0.2294\pm 0.0059$	$0.3543\pm 0.0449$	$0.3316\pm 0.0327$

Table 1: Temporal differentiation on 15 held-out donors, covering 30 prediction requests in the 2,009-gene evaluation space. Scores are aggregated across donors and requested times within each run. Entries report mean

\pm

standard deviation over three randomized test runs with fixed trained models.

	Seen 2/2		Seen 1/2		Seen 0/2		Seen 0/1
	20 conditions		20 conditions		16 conditions		11 conditions
Method	L2 $\downarrow$	$\Delta r\uparrow$	L2 $\downarrow$	$\Delta r\uparrow$	L2 $\downarrow$	$\Delta r\uparrow$	L2 $\downarrow$	$\Delta r\uparrow$
Control	5.6384	0.0011	5.5351	0.0114	4.7860	0.0110	3.5682	0.0113
Additive	3.6163	0.8719	NA		NA		NA
scGPT-scratch	3.1564	0.8635	4.1885	0.6614	4.1235	0.5237	3.4632	0.4203
GEARS	3.8881	0.7330	4.7681	0.4596	4.2786	0.5081	3.4356	0.3338

Table 2: Genetic prediction by holdout setting. Means use the test-repeat protocol in Section 5.1 ; each setting weights its conditions equally. Additive applies only to Seen 2/2; NA denotes an inapplicable comparison. Bold marks the best mean within each setting and metric. Complete metrics are in Table S2 .

Method	Mean L2 $\downarrow$	$\Delta r\uparrow$	pEnergy $\downarrow$	pMMD $\downarrow$	DE@100 $\uparrow$
Conditional MLP	4.8777 $\pm$ 0.0455	0.2254 $\pm$ 0.0190	0.2260 $\pm$ 0.0095	0.0317 $\pm$ 0.0005	0.3215 $\pm$ 0.0228
CFM without OT	4.6357 $\pm$ 0.0285	0.3848 $\pm$ 0.0056	0.2219 $\pm$ 0.0094	0.0345 $\pm$ 0.0027	0.2626 $\pm$ 0.0054
chemCPA adapter	5.5117 $\pm$ 0.1670	0.3827 $\pm$ 0.0122	0.3484 $\pm$ 0.0358	0.0437 $\pm$ 0.0029	0.5139 $\pm$ 0.0098
scDFM adapter	7.7612 $\pm$ 0.5215	0.2293 $\pm$ 0.0220	0.8281 $\pm$ 0.1396	0.0747 $\pm$ 0.0079	0.5579 $\pm$ 0.0034
CellFlow adapter	4.2875 $\pm$ 0.0125	0.5608 $\pm$ 0.0002	9.2228 $\pm$ 0.0121	0.2714 $\pm$ 0.0001	0.3465 $\pm$ 0.0002
TempoBridge	4.2478 $\pm$ 0.0470	0.5977 $\pm$ 0.0047	0.2123 $\pm$ 0.0193	0.0327 $\pm$ 0.0036	0.5471 $\pm$ 0.0129

Table 3: Unseen-compound response prediction on sci-Plex3 (248 equally weighted test conditions). Values are mean

\pm

sample SD over fixed-checkpoint test repeats (Section 5.1 ). pEnergy and pMMD use a common 50-dimensional Gaussian random projection (seed 42), with MMD bandwidth calibrated on training data. Baseline adapters are project implementations; bold marks the best mean in each column.

Model or setting	Branch acc. (%) $\uparrow$	Energy $\downarrow$
No context	$50.00\pm 0.00$	$0.4575\pm 0.0012$
Swapped context	$1.96\pm 0.40$	$3.3299\pm 0.1760$
TempoBridge	$98.04\pm 0.40$	$0.0054\pm 0.0004$

Table 4: Controlled source-dependent transition ambiguity. Results are mean

\pm

sample SD across three test runs of one fixed checkpoint per trained arm. Branch accuracy evaluates shared synthetic cells; Energy evaluates the full population. Correct and swapped contexts use the same TempoBridge checkpoint.

Appendix figures & tables22 assets

Supplementary material from the paper’s appendix.

Appendix

Task	Source population	Transition descriptor	Target population and evaluation setting
Temporal differentiation	Day 0 cells from a held-out donor	Requested target time	Day 1 or Day 2 population of the same donor
Genetic perturbation	Fixed K562 control population	Unordered set of one or two perturbed genes	Perturbed population under controlled component exposure
Drug response	Matched vehicle-control population	Molecular description, dose, treatment time, and cell line	Treated population for a compound excluded from training and validation

Appendix

Table S1: Task-specific instances of the conditional population prediction problem. Each task uses an independently trained model and its own gene space. The tasks share a common formulation, but not model parameters.

Seen 2/2: 20 test conditions
Method	Mean L2 $\downarrow$	$\Delta r\uparrow$	Energy $\downarrow$	DE $\rho\uparrow$
Control	5.6384	0.0011	1.8371	0.0378
Additive	3.6163	0.8719	0.9871	0.8956
scGPT-scratch	3.1564	0.8635	7.8094	0.9034
GEARS	3.8881	0.7330	0.9807	0.7925
CPA	5.0754	0.4594	7.2051	0.6198

Appendix

Table S2: Complete genetic metrics by holdout setting. For learned methods, each entry is the mean across test seeds 42, 123, and 2026 using the fixed checkpoint for that training setting, after condition-level averaging within each test run. Control and Additive are deterministic. Additive uses the observed single-gene responses and applies only to Seen 2/2. NA denotes an undefined metric for Control or an inapplicable comparison for Additive. Bold marks the best mean for each setting and metric. Seen 0/1 reuses the Seen 0/2 checkpoints. Control copies a target-sized prefix of the fixed source panel; its effect correlations exclude undefined values, as detailed in Appendix D.6 .

Method	Mean L2 $\downarrow$	$\Delta r\uparrow$	Energy $\downarrow$	DE $\rho\uparrow$
Control	4.8819	0.0087	1.4380	NA
scGPT-scratch	3.7329	0.6172	7.9229	0.7474
GEARS	4.0926	0.5086	1.0400	0.6848
CPA	5.1841	0.3684	7.5142	0.5636
CellFlow	3.8961	0.6158	2.8048	0.7089
scDFM	4.5115	0.5608	1.2054	0.6945

Appendix

Table S3: Genetic perturbation prediction averaged over four settings: Seen 2/2 (two seen genes; 20 conditions), Seen 1/2 (one seen and one unseen gene; 20 conditions), Seen 0/2 (two unseen genes; 16 conditions), and Seen 0/1 (one unseen gene; 11 conditions). For each method and metric, the reported value is the arithmetic mean of the four setting-level scores, giving each setting equal weight. Each setting-level score first averages test conditions within each run, then averages test seeds 42, 123, and 2026 using one fixed checkpoint per learned method and training setting. Only means are reported; no cross-setting SD is computed. DE

\rho

denotes Spearman correlation between predicted and observed log-fold changes on reference DE genes. Control is deterministic; NA indicates an undefined four-setting average. Additive is reported in Table S2 for Seen 2/2; its four-setting average is not defined. Seen 0/1 reuses the Seen 0/2 checkpoints without retraining.

Variant	MMD $\downarrow$	Energy $\downarrow$	$\Delta r\uparrow$	DE@100 $\uparrow$
Random-pairing flow	$0.4145\pm 0.0340$	$0.1446\pm 0.0063$	$0.6080\pm 0.0102$	$0.5316\pm 0.0116$
Static OT residual	$0.3848\pm 0.0207$	$0.1350\pm 0.0049$	$0.6159\pm 0.0105$	$0.5071\pm 0.0105$
Full flow + OT	$\mathbf{0.3626\pm 0.0143}$	$\mathbf{0.1291\pm 0.0047}$	$\mathbf{0.6284\pm 0.0115}$	$\mathbf{0.5624\pm 0.0110}$

Appendix

Table S4: Temporal transport-formulation comparisons under the same donor, gene-space, and evaluation protocol as Table 1 . Entries report mean

\pm

sample SD over three randomized test runs of one fixed checkpoint per variant (test seeds 42, 123, and 2026), using the same run-level aggregation as the temporal main comparison.

Task	Context from source cells	Structured descriptor fields	Not supplied as predictor input
Temporal	Day 0 population from the requested donor	Endpoint times; requested time through the integration horizon	Donor identity; replicate label
Genetic	Matched K562 control population	Perturbed genes; control/single/combination type	Combination identity hash; replicate label
Drug	Matched vehicle-control population	Molecular feature, dose, treatment time, cell line	Drug identity in the unseen-compound setting; replicate label

Appendix

Table S5: Conditioning interface used by the three task instances.

Component	Setting
Expression encoder; cell latent	MLP $5041\rightarrow 512\rightarrow 256$
Decoder	MLP $256\rightarrow 512\rightarrow 5041$ ; Softplus
Perturbation representation	Separate 512-dimensional gene embeddings; mean pooling
Dropout	Encoder/decoder 0.1; vector field 0
OT	Median-normalized squared latent cost; $\varepsilon=0.05$ ; 30 iterations
Batch	8 conditions; 128 source and target cells per record

Appendix

Table S6: Shared configuration for the nine genetic runs. Each holdout regime is trained independently with seeds 42, 123, and 2026.

Task	Genes	Latent	Source encoder	Solver	Steps
Temporal	2,009	256	Trainable	Heun	32
Genetic	5,041	256	Trainable	Euler	8
Drug	2,000	512	Frozen in stage B	Heun	16

Appendix

Table S7: Task-specific representation and inference settings.

Metric	Seed 42	Seed 123	Seed 2026	Mean	SD
L2 $\downarrow$	4.515	4.498	4.513	4.509	0.010
MSE $\downarrow$	0.011	0.011	0.011	0.011	$<0.001$
MAE $\downarrow$	0.074	0.074	0.075	0.074	$<0.001$
Gene $r\uparrow$	0.976	0.976	0.977	0.976	$<0.001$
$\Delta r\uparrow$	0.418	0.417	0.441	0.425	0.014
DE $\rho\uparrow$	0.340	0.285	0.277	0.301	0.034

Appendix

Table S8: Seed-level Stage-B results for TempoBridge on the compound-disjoint sci-Plex3 split, using a shared frozen seed-42 expression backbone and condition warm-start. Checkpoints were selected on validation data before evaluation on the compound-disjoint split. Each seed’s score weights conditions equally; SD is the sample SD across the three training seeds, not a compound-bootstrap interval.

Method	pEnergy $\downarrow$	pMMD $\downarrow$	L2 $\downarrow$	$\Delta r\uparrow$	DE@100 $\uparrow$	Var. $r\uparrow$	Cov. $r\uparrow$
Stage-B TempoBridge	0.197 $\pm$ 0.010	0.031 $\pm$ 0.001	4.509 $\pm$ 0.010	0.425 $\pm$ 0.014	0.267 $\pm$ 0.013	0.909 $\pm$ 0.003	0.219 $\pm$ 0.002
Main-pipeline TempoBridge	0.212 $\pm$ 0.019	0.033 $\pm$ 0.004	4.248 $\pm$ 0.047	0.598 $\pm$ 0.005	0.547 $\pm$ 0.013	0.908 $\pm$ 0.004	0.221 $\pm$ 0.001
Conditional MLP	0.226 $\pm$ 0.010	0.032 $\pm$ 0.001	4.878 $\pm$ 0.046	0.225 $\pm$ 0.019	0.322 $\pm$ 0.023	0.937 $\pm$ 0.000	0.343 $\pm$ 0.001
Conditional CFM (no OT)	0.222 $\pm$ 0.009	0.034 $\pm$ 0.003	4.636 $\pm$ 0.029	0.385 $\pm$ 0.006	0.263 $\pm$ 0.006	0.904 $\pm$ 0.002	0.217 $\pm$ 0.019

Appendix

Table S9: Drug-response main evaluation and supplementary Stage-B analysis. All rows weight biological conditions equally. The Stage-B row averages transition modules fitted with training seeds 42, 123, and 2026 on a shared frozen seed-42 expression backbone and condition warm-start. The main-pipeline and baseline rows evaluate one fixed checkpoint per method with test seeds 42, 123, and 2026, as in Table 3 ; the main-pipeline row additionally reports variance and covariance correlations. Their SDs describe training-seed and test-run variation, respectively. Cross-row differences do not isolate an OT component effect.

Arm	pEnergy $\downarrow$	pMMD $\downarrow$	L2 $\downarrow$	$\Delta r\uparrow$	DE $\rho\uparrow$	DE@100 $\uparrow$
Full	0.197 $\pm$ 0.010	0.031 $\pm$ 0.001	4.509 $\pm$ 0.010	0.425 $\pm$ 0.014	0.301 $\pm$ 0.034	0.267 $\pm$ 0.013
No source context	0.193 $\pm$ 0.005	$0.031\,(\mathrm{SD}<0.001)$	4.506 $\pm$ 0.017	0.422 $\pm$ 0.004	0.289 $\pm$ 0.046	0.261 $\pm$ 0.003
No cell line	0.195 $\pm$ 0.003	$0.031\,(\mathrm{SD}<0.001)$	4.539 $\pm$ 0.006	0.414 $\pm$ 0.003	0.295 $\pm$ 0.055	0.260 $\pm$ 0.005
Neither	0.196 $\pm$ 0.004	$0.031\,(\mathrm{SD}<0.001)$	4.538 $\pm$ 0.008	0.415 $\pm$ 0.004	0.295 $\pm$ 0.052	0.270 $\pm$ 0.003

Appendix

Table S10: Matched

2\times 2

conditioning ablation on compound-disjoint sci-Plex3 in the fixed-backbone Stage-B setting. (a) Equal condition weights within each training seed; mean

\pm

sample SD over seeds 42, 123, and 2026. (b) Compound-weighted paired differences, Full minus No source context, with their 95% intervals; positive values favor Full. These differences use compound weights and are not obtained by subtracting the displayed condition-weighted means. Removing a condition replaces its vector with zeros without changing model capacity.

Evaluation space	Energy win rate	Mean Energy reduction	MMD win rate
Gaussian 20D	100.000%	7.530%	20.000%
Gaussian 50D	100.000%	8.280%	40.000%
Gaussian 100D	100.000%	9.640%	60.000%
Gaussian 200D	100.000%	10.800%	40.000%
All 22 spaces	95.500% (21/22)	8.180%	36.400% (8/22)

Appendix

Table S11: Fixed-backbone TempoBridge projection-space sensitivity relative to Conditional MLP. Each Gaussian dimension uses five train-only projection seeds. The final row also includes PCA-50 and PCA-100.

Method	L2 $\downarrow$	$\Delta r\uparrow$	DE $\rho\uparrow$	pMMD $\downarrow$	pEnergy $\downarrow$
TempoBridge	4.677	0.414	0.161	0.034	0.223
Conditional CFM (no OT)	4.793	0.387	0.171	0.035	0.242
Conditional MLP	5.060	0.239	0.361	0.034	0.259
Fingerprint KNN	5.187	0.225	0.388	0.037	0.279
chemCPA adapter	5.620	0.368	0.386	0.046	0.386

Appendix

Table S12: Supplementary scaffold-disjoint evaluation for seed 42. The test split contains 17 compounds and 220 biological conditions. This single-seed analysis is not used for the main compound-disjoint claim.

Metric	Full context	No context	Relative change
Formal MMD $\downarrow$	0.378 $\pm$ 0.021	0.397 $\pm$ 0.048	4.720%
Energy $\downarrow$	0.135 $\pm$ 0.005	0.139 $\pm$ 0.013	3.100%
$\Delta$ Pearson $\uparrow$	0.625 $\pm$ 0.005	0.639 $\pm$ 0.010	-2.170%
Variance Pearson $\uparrow$	0.622 $\pm$ 0.010	0.613 $\pm$ 0.047	1.620%
Covariance Pearson $\uparrow$	0.419 $\pm$ 0.006	0.421 $\pm$ 0.005	-0.470%
DE@100 $\uparrow$	0.515 $\pm$ 0.005	0.529 $\pm$ 0.007	-2.730%

Appendix

Table S13: Separately matched source-context ablation on the 15-donor temporal cohort in the 2,009-gene space. Both arms were retrained under the same training configuration and seeds, independently of the main-table models; the only difference is whether the pooled source context is supplied. Values are mean

\pm

sample standard deviation over three training seeds. Relative change is signed so that positive values favor the full-context arm.

Metric	Correct	Incorrect mean	Effect	95% CI	Donors won
Energy $\downarrow$	0.138	0.142	0.004	[0.002,0.007]	12/15
Formal MMD $\downarrow$	0.385	0.392	0.007	[0.004,0.009]	12/15
$\Delta r\uparrow$	0.627	0.616	0.011	[0.003,0.021]	11/15
DE@100 $\uparrow$	0.512	0.503	0.009	[0.004,0.014]	12/15

Appendix

Table S14: Temporal donor context-swap intervention. The correct context is compared with the mean over the 14 incorrect donor contexts while query cells, requested time, checkpoint, decoder, and target remain fixed within each donor/day/seed comparison. Effects average the two days and evaluations with seeds 42, 123, and 2026, and are reported in the direction favoring the correct context; intervals use donor-level paired bootstrap conditional on the fitted checkpoints and context bank.

Method	Energy $\downarrow$	Formal MMD $\downarrow$	Sink. $\downarrow$	Gene $r$ $\uparrow$
scVIDR (time-adapted)	$0.294\pm 0.005$	$0.476\pm 0.006$	$0.195\pm 0.002$	$0.726\pm 0.005$

Appendix

Table S15: Auxiliary 2,009-gene result for the time-adapted scVIDR implementation on the fixed 15-donor cohort with target-matched cardinality. Values follow the main temporal test-repeat protocol: mean

\pm

sample standard deviation over test seeds 42, 123, and 2026.

Method	Energy $\downarrow$	Formal MMD $\downarrow$	Gene $r$ $\uparrow$	Var. $r$ $\uparrow$	DE@100 $\uparrow$
Endpoint interpolation	0.225	0.364	0.755	0.632	0.699
PCA interpolation	0.290	0.466	0.724	0.598	0.688

Appendix

Table S16: Non-deployable endpoint references. Both methods read held-out Day 3 expression and are excluded from the external-method ranking.

	Energy $\downarrow$		Formal MMD $\downarrow$		DE@100 $\uparrow$
Method	Day 1	Day 2	Day 1	Day 2	Day 1	Day 2
TempoBridge Full Flow	0.131 $\pm$ 0.006	0.128 $\pm$ 0.004	0.373 $\pm$ 0.015	0.353 $\pm$ 0.014	0.501 $\pm$ 0.013	0.624 $\pm$ 0.009
Random-pairing Flow	0.149 $\pm$ 0.007	0.140 $\pm$ 0.005	0.429 $\pm$ 0.037	0.401 $\pm$ 0.031	0.426 $\pm$ 0.014	0.637 $\pm$ 0.010
Static OT residual	0.131 $\pm$ 0.002	0.139 $\pm$ 0.008	0.385 $\pm$ 0.017	0.385 $\pm$ 0.024	0.401 $\pm$ 0.016	0.614 $\pm$ 0.009

Appendix

Table S17: Request-time decomposition in the 2,009-gene space on the fixed 15-donor cohort. Within each randomized test run, metrics are averaged equally across the 15 donor-specific requests at each day. Values are mean

\pm

sample standard deviation over three randomized test runs of one fixed checkpoint per variant (test seeds 42, 123, and 2026), matching the main temporal evaluation.

Steps / calls	Energy $\downarrow$	Formal MMD $\downarrow$	Time (s) $\downarrow$
4 / 8	0.259	0.405	0.087
8 / 16	0.259	0.405	0.126
16 / 32	0.259	0.405	0.211
32 / 64	0.259	0.405	0.363

Appendix

Table S18: Heun solver sensitivity for a frozen seed-42 Full Flow checkpoint on three validation donors (six requests), scored on the fixed 2,009-gene panel with target-matched cardinality. Scores average the six requests. One Heun step uses two velocity-network evaluations. Timing is seconds per 1,000 generated cells.

Arm	Seed	$D_{\mathrm{ctx}}$	$S_{\mathrm{ctx}}$	Shared error	Branch acc.	Energy	MMD
Descriptor-only	42	0.000	0.000	2.001	0.500	0.457	0.273
	123	0.000	0.000	2.001	0.500	0.456	0.273
	2026	0.000	0.000	2.001	0.500	0.459	0.272
	31415	0.000	0.000	2.001	0.500	0.458	0.272
	27182	0.000	0.000	2.000	0.500	0.457	0.272
Swapped context	42	3.899	-3.882	3.941	0.013	3.430	0.779

Appendix

Table S19: Checkpoint-level results for the controlled source-context experiment. Seed indexes five training checkpoints, separately from the fixed-model randomized test repeats in Table 4 . Branch accuracies are tabulated as fractions.

S_{\mathrm{ctx}}

is a post hoc directional metric computed from fixed predictions without retraining or checkpoint reselection.

Figure S1: Velocity fields at $\tau=0.5$ for seed 42. The context-free field is identical for A and B at a shared state; empirical contexts produce distinct fields, and exchanging the context input exchanges the field. These are diagnostics in the controlled synthetic latent system.

Figure S2: Model trajectories of the identical shared source states for seed 42. TempoBridge separates the requested branches, while the context-free model overlaps and swapped context reverses the separation. The curves are synthetic ODE trajectories, not reconstructed biological lineages.

Figure S3: Velocity $y$ -component at the identical state $z^{\star}=(0,0)$ across flow time for seed 42. The context-free field returns identical velocities for A and B. TempoBridge assigns opposite directions, and swapping the empirical contexts reverses them. Dashed lines mark reference shared-component centroid displacements $+2$ and $-2$ over the unit transport interval, not exact conditional velocities at every probed time.

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Single-cell perturbation modeling predicts how genetic or chemical interventions change cellular states across cells and contexts.

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From Snapshots to Trajectories: Learning Single-Cell Gene Expression Dynamics via Conditional Flow Matching

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Latent Dynamics Modeling Conditional Flow Matching Single-Cell Transcriptomics

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Single-cell RNA sequencing (scRNA-seq) provides high-dimensional profiles of cellular states, enabling data-driven modeling of cellular dynamics over time. In practice, time-resolved scRNA-seq is collected at only a few discrete time points as unpaired snapshot populations, leaving substantial temporal gaps. This motivates trajectory inference at unmeasured time points. Existing methods mainly follow two directions, optimal-transport (OT) alignment provides distribution-level matching between observed snapshots, while continuous-time generative models support forecasting via learned dynamics. However, two challenges remain: (i) unpaired snapshots render local transitions between adjacent time points ambiguous, leading to unstable supervision; and (ii) long-horizon prediction relies on repeated integration, where small modeling errors compound and cause distribution drift. To address these challenges, we propose single-cell Flow Matching (scFM), a latent generative framework based on coupling-conditioned flow matching. First, we compute entropically regularized OT couplings between adjacent snapshots and use them to construct soft, weighted flow-matching targets for learning time-dependent velocity fields. Second, we learn bidirectional velocity fields and leverage their consistency to refine couplings and improve temporal coherence under sparse supervision. Third, we introduce distribution-level alignment and latent dynamic regularization to anchor long rollouts and mitigate drift. Experiments on real-world time-series scRNA-seq datasets show that scFM consistently improves distributional prediction performance for both temporal interpolation and extrapolation. Moreover, scFM yields more accurate trajectory reconstruction and temporally coherent visualizations where intermediate time points are absent, indicating a more faithful recovery of underlying temporal gene expression dynamics.

Abstract

Single-Cell Perturbation Modeling

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