# Inferring biological processes with intrinsic noise from cross-sectional data

arXiv: https://arxiv.org/abs/2410.07501 · HTML: https://mlsanity.com/paper/2410.07501/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 93 references that are in the map.
- First posted on arXiv 10 Oct 2024.

## Builds on (most cited first, 13 of 13)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Deep learning generalizes because the parameter-function map is biased towards simple functions](https://mlsanity.com/paper/1805.08522/) (2018)
- [Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs](https://mlsanity.com/paper/2007.01138/) (2020)
- [Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation](https://mlsanity.com/paper/2006.00702/) (2020)
- [Scalable Unbalanced Optimal Transport using Generative Adversarial Networks](https://mlsanity.com/paper/1810.11447/) (2018)
- [Towards a mathematical theory of trajectory inference](https://mlsanity.com/paper/2102.09204/) (2021)
- [Trajectory Inference via Mean-field Langevin in Path Space](https://mlsanity.com/paper/2205.07146/) (2022)
- [Deep learning probability flows and entropy production rates in active matter](https://mlsanity.com/paper/2309.12991/) (2023)

## Built on by (most cited first, 9 of 9)

- [Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshots](https://mlsanity.com/paper/2410.22729/) (2024)
- [Modeling Cell Dynamics and Interactions with Unbalanced Mean Field Schr"odinger Bridge](https://mlsanity.com/paper/2505.11197/) (2025)
- [Variational Regularized Unbalanced Optimal Transport: Single Network, Least Action](https://mlsanity.com/paper/2505.11823/) (2025)
- [Integrating Dynamical Systems Modeling with Spatiotemporal scRNA-seq Data Analysis](https://mlsanity.com/paper/2503.11347/) (2025)
- [WFR-FM: Simulation-Free Dynamic Unbalanced Optimal Transport](https://mlsanity.com/paper/2601.06810/) (2026)
- [Inferring stochastic dynamics with growth from cross-sectional data](https://mlsanity.com/paper/2505.13197/) (2025)
- [Learning non-equilibrium diffusions with Schr"odinger bridges: from exactly solvable to simulation-free](https://mlsanity.com/paper/2505.16644/) (2025)
- [TracingFlow: A Simulation-Free Trajectory Inference Framework Based on Second-Order Dynamics](https://mlsanity.com/paper/2608.21070/) (2026)
- [Identifying Stochastic Dynamics from Non-Sequential Data (DyNoSeD)](https://mlsanity.com/paper/2502.17690/) (2025)

## Abstract (arXiv)

Inferring dynamical models from data continues to be a significant challenge in computational biology, especially given the stochastic nature of many biological processes. We explore a common scenario in omics, where statistically independent cross-sectional samples are available at a few time points, and the goal is to infer the underlying diffusion process that generated the data. Existing inference approaches often simplify or ignore noise intrinsic to the system, compromising accuracy for the sake of optimization ease. We circumvent this compromise by inferring the phase-space probability flow that shares the same time-dependent marginal distributions as the underlying stochastic process. Our approach, probability flow inference (PFI), disentangles force from intrinsic stochasticity while retaining the algorithmic ease of ODE inference. Analytically, we prove that for Ornstein-Uhlenbeck processes the regularized PFI formalism yields a unique solution in the limit of well-sampled distributions. In practical applications, we show that PFI enables accurate parameter and force estimation in high-dimensional stochastic reaction networks, and that it allows inference of cell differentiation dynamics with molecular noise, outperforming state-of-the-art approaches.