Title: Count Bridges enable Modeling and Deconvolving Transcriptomics
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: ordinal data, diffusion, schrodinger bridge, flow matching, single cell genomics, spatial transcriptomics

Abstract: Many modern biological assays, including RNA sequencing, yield integer-valued counts that reflect the number of RNA molecules detected. These measurements are often not at the desired resolution: while the unit of interest is typically a single cell, many RNA sequencing and imaging technologies produce counts aggregated over sets of cells. 
Although recent generative frameworks such as diffusion and flow matching have been extended to non-Euclidean and discrete settings, it remains unclear how best to model integer-valued data or how to systematically deconvolve aggregated observations.
We introduce Count Bridges, a stochastic bridge process on the integers that provides an exact, tractable analogue of diffusion-style models for count data, with closed-form conditionals for efficient training and sampling. We extend this framework to enable direct training from aggregated measurements via an Expectation-Maximization-style approach that treats unit-level counts as latent variables.
We demonstrate state-of-the-art performance on integer distribution matching benchmarks, comparing against flow matching and discrete flow matching baselines across various metrics. We then apply Count Bridges to two large-scale problems in biology: modeling single-cell gene expression data at the nucleotide resolution, with applications to deconvolving bulk RNA-seq, and resolving multicellular spatial transcriptomic spots into single-cell count profiles. Our methods offer a principled foundation for generative modeling and deconvolution of biological count data across scales and modalities.

TL;DR: We extend diffusion models to count data.