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Flow Matching for Count Data

NeurIPS 2026 · Probabilistic and scientific modeling › Variational and generative sampling · approach: Flow matching and flow sampling · 0 citations (OpenAlex)

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Proposes count-FM, a flow-matching framework for count data using a continuous-time birth-death CTMC with local unit jumps and a conditional binomial bridge, evaluated on a 2D simulation, scRNA-seq (Dentate Gyrus) and hc-3 neural spike trains.

Problem

Generative modeling and transport between high-dimensional count distributions (e.g., scRNA-seq counts, neural spike trains) where categorical-state or continuous-relaxation methods are inefficient or unnatural for large count ranges.

Approach

Model transport directly in count space via a birth-death CTMC with local ±1 jumps; train marginal transition rates by simulation-free matching to closed-form conditional rates from a coordinatewise binomial bridge, parameterizing only 2d rates (birth and death per coordinate) regardless of count range.

Key results

• In the 2D simulation, count-FM-OT achieves the best W1 (1.685) and W2 (2.341) with 2,372 parameters versus 15,306 for SEDD/D3PM-type baselines.
• On Dentate Gyrus unconditional generation, count-FM achieves W2 20.456 and MMD 0.0185, best among seven baselines, including scLDM (W2 20.739) and scVI (20.687).
• On hc-3 conditional generation, count-FM with w=1 gives lowest RMSE_mu (0.026) and Cov_F (0.344) versus Poisson MLP (Cov_F 0.564).

Surprising findings

• SEDD obtains the lowest MMD despite a higher W2 than count-FM variants in the simulation.
• Guidance scale w=2 gives the highest place-field contrast but worsens calibration metrics.

Limitations

• Conditional binomial bridge is deterministic-ish and may be too rigid to explore plausible intermediate paths.
• First-order local-jump sampler has discretization error when jump rates are large; large displacements need more steps.
• Marginal rate matching averages conditional dynamics when futures are indistinguishable from current state.

Experimental setup

Datasets: Dentate Gyrus scRNA-seq CRCNS hc-3 (ec013.719) two-dimensional Gamma-Poisson mixture simulation piriform cortex odor-response spike trains

Benchmarks: two-dimensional Gamma-Poisson mixture simulation Dentate Gyrus scRNA-seq unconditional generation hc-3 linear-track conditional generation

Metrics: W1 W2 MMD RBF RMSE mean RMSE variance RMSE zero fraction covariance Frobenius error contrast marker-gene MAE

Baselines: Dirichlet-FM discrete-FM D3PM tauLDR SEDD Poisson-JUMP scVI scDiffusion scLDM DCM CFGen Poisson MLP

Builds on: OT-CFM classifier-free guidance tau-leaping discrete flow matching path-space KL for CTMCs

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