# Stochastic Flow Map for Count Data

arXiv: https://arxiv.org/abs/2609.23290 · HTML: https://mlsanity.com/paper/2609.23290/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 45 references that are in the map.
- First posted on arXiv 20 Sep 2026.

## Builds on (most cited first, 23 of 23)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioning](https://mlsanity.com/paper/2208.04202/) (2022)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [Flow map matching with stochastic interpolants: A mathematical framework for consistency models](https://mlsanity.com/paper/2406.07507/) (2024)
- [How to build a consistency model: Learning flow maps via self-distillation](https://mlsanity.com/paper/2505.18825/) (2025)
- [Generator Matching: Generative modeling with arbitrary Markov processes](https://mlsanity.com/paper/2410.20587/) (2024)
- [Categorical Flow Maps](https://mlsanity.com/paper/2602.12233/) (2026)
- [Discrete Flow Maps](https://mlsanity.com/paper/2604.09784/) (2026)
- [Self-conditioned Flow Map Language Models via Fixed-point Flows](https://mlsanity.com/paper/2607.00714/) (2026)
- [scPPDM: A Diffusion Model for Single-Cell Drug-Response Prediction](https://mlsanity.com/paper/2510.11726/) (2025)
- [Count Bridges enable Modeling and Deconvolving Transcriptomic Data](https://mlsanity.com/paper/2603.04730/) (2026)
- [Flow Matching for Count Data](https://mlsanity.com/paper/2605.07746/) (2026)
- [CountsDiff: A Diffusion Model on the Natural Numbers for Generation and Imputation of Count-Based Data](https://mlsanity.com/paper/2604.03779/) (2026)
- [SpikeProphecy: A Large-Scale Benchmark for Autoregressive Neural Population Forecasting](https://mlsanity.com/paper/2605.12992/) (2026)

## Built on by (most cited first, 1 of 1)

- [Jumping up and down: Denoiser diffusion models for discrete ordinal data](https://mlsanity.com/paper/2610.02754/) (2026)

## Abstract (arXiv)

High-dimensional count data are common in scientific applications, but most diffusion and flow models are designed for continuous or categorical data, and generation often requires many sequential model evaluations. We propose Count Flow Map, a generative model that learns finite-time transitions directly in count space for one- or few-step generation. Our model directly learns stochastic transitions over finite time intervals, using Poisson births and Binomial deaths to preserve nonnegative integer counts without a predefined maximum. These transition models are trained to match the underlying local birth--death dynamics and to maintain consistency across step sizes. We characterize the connection between local dynamics and finite-time transition consistency and derive a bound on the generation error. After validating Count Flow Map in several simulations, including a high-dimensional, high-count setting, we apply it to single-cell drug perturbation prediction and neural population forecasting, where it captures perturbation responses and supports forecasts of high-activity events with only one or a few model evaluations. Together, these experiments demonstrate that Count Flow Map enables high-quality generation directly in count space across inference budgets, from one-step to few-step generation, using a single trained model.