Gradient-Flow SDEs Have Unique Transient Population Dynamics

Vincent Guan, Joseph Janssen, Nicolas Lanzetti, Antonio Terpin, Geoffrey Schiebinger, Elina Robeva
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:2449-2457, 2026.

Abstract

Identifying the drift and diffusion of an SDE from its population dynamics is a notoriously challenging task. Researchers in machine learning and single-cell biology have only been able to prove a partial identifiability result: for potential-driven SDEs, the gradient-flow drift can be identified from temporal marginals if the Brownian diffusivity is already known. Existing methods therefore assume that the diffusivity is known a priori, despite it being unknown in practice. We dispel the need for this assumption by providing a complete characterization of identifiability: the gradient-flow drift and Brownian diffusivity are jointly identifiable from temporal marginals if and only if the process is observed outside of equilibrium. Given this fundamental result, we propose nn-APPEX, the first Schr{ö}dinger Bridge–based inference method that can simultaneously learn the drift and diffusion of a gradient-flow SDE solely from observed marginals. Extensive experiments show that nn-APPEX’s ability to adjust its diffusion estimate enables accurate inference, while previous Schr{ö}dinger Bridge methods obtain biased drift estimates due to their assumed, and likely incorrect, diffusion.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-guan26a, title = { Gradient-Flow SDEs Have Unique Transient Population Dynamics }, author = {Guan, Vincent and Janssen, Joseph and Lanzetti, Nicolas and Terpin, Antonio and Schiebinger, Geoffrey and Robeva, Elina}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {2449--2457}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/guan26a/guan26a.pdf}, url = {https://proceedings.mlr.press/v300/guan26a.html}, abstract = { Identifying the drift and diffusion of an SDE from its population dynamics is a notoriously challenging task. Researchers in machine learning and single-cell biology have only been able to prove a partial identifiability result: for potential-driven SDEs, the gradient-flow drift can be identified from temporal marginals if the Brownian diffusivity is already known. Existing methods therefore assume that the diffusivity is known a priori, despite it being unknown in practice. We dispel the need for this assumption by providing a complete characterization of identifiability: the gradient-flow drift and Brownian diffusivity are jointly identifiable from temporal marginals if and only if the process is observed outside of equilibrium. Given this fundamental result, we propose nn-APPEX, the first Schr{ö}dinger Bridge–based inference method that can simultaneously learn the drift and diffusion of a gradient-flow SDE solely from observed marginals. Extensive experiments show that nn-APPEX’s ability to adjust its diffusion estimate enables accurate inference, while previous Schr{ö}dinger Bridge methods obtain biased drift estimates due to their assumed, and likely incorrect, diffusion. } }
Endnote
%0 Conference Paper %T Gradient-Flow SDEs Have Unique Transient Population Dynamics %A Vincent Guan %A Joseph Janssen %A Nicolas Lanzetti %A Antonio Terpin %A Geoffrey Schiebinger %A Elina Robeva %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-guan26a %I PMLR %P 2449--2457 %U https://proceedings.mlr.press/v300/guan26a.html %V 300 %X Identifying the drift and diffusion of an SDE from its population dynamics is a notoriously challenging task. Researchers in machine learning and single-cell biology have only been able to prove a partial identifiability result: for potential-driven SDEs, the gradient-flow drift can be identified from temporal marginals if the Brownian diffusivity is already known. Existing methods therefore assume that the diffusivity is known a priori, despite it being unknown in practice. We dispel the need for this assumption by providing a complete characterization of identifiability: the gradient-flow drift and Brownian diffusivity are jointly identifiable from temporal marginals if and only if the process is observed outside of equilibrium. Given this fundamental result, we propose nn-APPEX, the first Schr{ö}dinger Bridge–based inference method that can simultaneously learn the drift and diffusion of a gradient-flow SDE solely from observed marginals. Extensive experiments show that nn-APPEX’s ability to adjust its diffusion estimate enables accurate inference, while previous Schr{ö}dinger Bridge methods obtain biased drift estimates due to their assumed, and likely incorrect, diffusion.
APA
Guan, V., Janssen, J., Lanzetti, N., Terpin, A., Schiebinger, G. & Robeva, E.. (2026). Gradient-Flow SDEs Have Unique Transient Population Dynamics . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:2449-2457 Available from https://proceedings.mlr.press/v300/guan26a.html.

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