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High-dimensional count data, such as single-cell RNA sequencing or neural spike trains, present unique challenges for generative modeling due to their discreteness, sparsity, and lack of a natural upper bound. Existing diffusion and flow-based models often struggle with these properties, either by requiring continuous approximations or by imposing artificial maximums on count values. Furthermore, these models typically require many sequential evaluations to generate a single sample, which is computationally expensive.
To address these limitations, the author introduces Count Flow Map. This model extends the existing count-FM framework—which learns infinitesimal birth-death rates—to learn finite-time transitions directly. By modeling stochastic transitions between arbitrary time points using Poisson births and Binomial deaths, the model ensures that generated samples remain nonnegative integers. The training objective combines local rate matching with Chapman-Kolmogorov consistency, which forces the model to maintain consistency across different time intervals, thereby enabling one- or few-step generation.
Count Flow Map demonstrates strong performance across various benchmarks. In 2-D and 32-D simulations, it achieves superior endpoint quality compared to existing discrete and continuous generative models, particularly when limited to a small number of function evaluations (NFE). In single-cell drug perturbation prediction, the model accurately recovers gene-expression responses to held-out drug doses with high distributional accuracy and minimal computational cost.
In neural population forecasting, Count Flow Map provides efficient next-bin predictions of spike counts. It captures complex dependencies between neurons, which is critical for accurately forecasting high-activity events. Compared to baseline methods, Count Flow Map achieves comparable forecast quality while being significantly faster, demonstrating its utility for real-time or large-scale scientific forecasting tasks.
This work provides a robust and efficient solution for generating count-valued data, a common data type in the biological and physical sciences. By enabling high-quality generation with very few model evaluations, Count Flow Map significantly reduces the inference cost of generative modeling for discrete data. Its ability to handle unbounded count spaces and maintain consistency across time scales makes it a versatile tool for researchers working with complex, high-dimensional count datasets.
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