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Joint Velocity-Growth Flow Matching for Single-Cell Dynamics Modeling
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Proposes Velocity-Growth Flow Matching (VGFM), jointly learning state-transition velocity and mass-growth fields for unbalanced single-cell snapshot dynamics via a two-period semi-relaxed OT reformulation, flow matching, and a W1 distribution-fitting loss.
Problem
Modeling single-cell population dynamics from unpaired, unbalanced snapshot data where cell proliferation and death change mass between time points, while avoiding costly simulation during training.
Approach
Decouples semi-relaxed OT into a two-period process (growth then transport), reparameterizes it into a joint velocity-and-growth dynamics on [0,1] that yields the same endpoint, and trains neural velocity and growth networks by simulation-free flow matching on OT-coupled samples, plus a Wasserstein distribution-fitting loss.
Key results
- On Simulation Gene (2D), VGFM achieves mean W1 0.046 and RME 0.006, versus 0.068 and 0.016 for DeepRUOT, the strongest baseline.
- On the 1000-dimensional Gaussian mixture, UDSB, TIGON and DeepRUOT do not converge, while VGFM reaches mean W1 3.010 and RME 0.037.
- On the EB (5D) hold-one-out task, VGFM gets mean W1 0.676 versus 0.713 for OT-MFM and 0.774 for DeepRUOT; on CITE 50D, OT-MFM (36.394) beats VGFM (37.386).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use VGFM instead of DeepRUOT | single-cell dynamics modeling · Simulation Gene (2D) | W1: 0.068 -> 0.046 | Helped |
| Use VGFM instead of DeepRUOT | single-cell dynamics modeling · Dyngen (5D) | RME: 0.199 -> 0.053 | Helped |
| Use VGFM instead of DeepRUOT | single-cell dynamics modeling · Gaussian (1000D) | W1: N/C -> 3.010 | Helped |
| Use VGFM instead of OT-MFM | single-cell dynamics modeling · EB (5D), hold-one-out | W1: 0.713 -> 0.676 | Helped |
| Use VGFM instead of OT-MFM | single-cell dynamics modeling · CITE (5D), hold-one-out | W1: 0.724 -> 0.745 | Hurt |
| Use VGFM instead of OT-MFM | single-cell dynamics modeling · CITE (50D), hold-one-out | W1: 36.394 -> 37.386 | Hurt |
| Add distribution fitting loss L_OT (ablation) | VGFM · EB (50D), t1 | W1: 8.915 -> 7.951 | Helped |
| Add distribution fitting loss L_OT (ablation) | VGFM · EB (50D), t1 | RME: 0.020 -> 0.089 | Hurt |
| Add joint velocity-growth matching loss L_VGFM (ablation) | VGFM · EB (50D), t1 | W1: 8.644 -> 7.951 | Helped |
| Add joint velocity-growth matching loss L_VGFM (ablation) | VGFM · EB (50D), t1 | RME: 0.650 -> 0.089 | Helped |
| Replace W1 fitting loss with Sinkhorn divergence (ablation) | VGFM · EB (50D), t1 | W1: 7.951 -> 7.902 | Helped |
| Replace W1 fitting loss with Sinkhorn divergence (ablation) | VGFM · EB (50D), t3 | RME: 0.019 -> 0.083 | Hurt |
Surprising findings
- On CITE 5D and 50D hold-out, VGFM does not beat OT-MFM, so the advantage is not uniform across real datasets.
Limitations
- Not fully simulation-free because the distribution-fitting W1 loss requires simulating trajectories through the learned ODE.
- The learned growth rate depends on observed cell counts and may capture non-biological effects.
- Growth is modeled as time-independent, justified via a Malthusian-model argument rather than biological priors.
Experimental setup
Datasets: Simulation Gene Dyngen Gaussian mixture (1000D) Embryoid Body CITE-seq Pancreas
Benchmarks: Simulation Gene Dyngen Gaussian mixture 1000D Embryoid Body CITE-seq Pancreas
Metrics: W1 distance relative mass error Pearson correlation
Baselines: OT-CFM OT-MFM SF2M UDSB TIGON DeepRUOT
Builds on: flow matching OT-CFM semi-relaxed optimal transport Wasserstein-Fisher-Rao
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