Flow Matching for Count Data
Abstract
High-dimensional count data arise in applications such as single-cell RNA sequencing and neural spike trains, where mappings between distributions across successive batches or time points form critical components of data analysis. The recent success of diffusion- and flow-based deep generative models for images, video, and text motivates extending these ideas to count-valued settings, but many existing methods either treat each count as a categorical state or transform counts into a continuous space, neither of which is natural or efficient when the count range is large. We propose count-FM, a flow-matching framework for count data based on a continuous-time birth-death process with local unit jumps. Count-FM learns marginal transitions efficiently in count space through simulation-free training of conditional transition rates, allowing transport between arbitrary count-distributed source and target populations. In simulation, count-FM variants achieve strong sample quality while using substantially fewer parameters. We further apply count-FM to scRNA-seq and neural spike-train data for unconditional generation, transport, and conditional generation. Across these tasks, count-FM yields improved sample quality, greater modeling efficiency, and interpretable transport paths.
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BibTeX
@misc{wei2026flow,
title = {{Flow Matching for Count Data}},
author = {Ganchao Wei and John Pearson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.07746},
eprint = {2605.07746},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.07746},
}
RIS
TY - UNPB
TI - Flow Matching for Count Data
AU - Ganchao Wei
AU - John Pearson
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2605.07746
UR - https://arxiv.org/abs/2605.07746
AB - High-dimensional count data arise in applications such as single-cell RNA sequencing and neural spike trains, where mappings between distributions across successive batches or time points form critical components of data analysis. The recent success of diffusion- and flow-based deep generative models for images, video, and text motivates extending these ideas to count-valued settings, but many existing methods either treat each count as a categorical state or transform counts into a continuous space, neither of which is natural or efficient when the count range is large. We propose count-FM, a flow-matching framework for count data based on a continuous-time birth-death process with local unit jumps. Count-FM learns marginal transitions efficiently in count space through simulation-free training of conditional transition rates, allowing transport between arbitrary count-distributed source and target populations. In simulation, count-FM variants achieve strong sample quality while using substantially fewer parameters. We further apply count-FM to scRNA-seq and neural spike-train data for unconditional generation, transport, and conditional generation. Across these tasks, count-FM yields improved sample quality, greater modeling efficiency, and interpretable transport paths.
ER -