# Conditional Flow Matching for Single-Neuron Electrophysiology: Capturing Multimodal Responses Across Stimuli

arXiv: https://arxiv.org/abs/2610.06520 · HTML: https://mlsanity.com/paper/2610.06520/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 7 of its 62 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 7 of 7)

- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10566/) (2017)
- [Progressive Distillation for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2202.00512/) (2022)
- [Physically constrained neural networks to solve the inverse problem for neuron models](https://mlsanity.com/paper/2209.11998/) (2022)
- [An efficient wavelet-based physics-informed neural network for multiscale problems](https://mlsanity.com/paper/2409.11847/) (2024)

## Abstract (arXiv)

Neurons of the brain exhibit a rich repertoire of electrophysiology dynamics with the same repeated stimulus eliciting very different voltage responses from the same cell. One common approach in biophysically detailed models is to capture this variability through ensembles of deterministic parametrizations, at a cost of hundreds of thousands of CPU hours. Existing machine learning surrogates inherit the same limitation, where a stimulus is mapped to a single voltage response. We address this challenge by learning a conditional generative model for single-neuron electrophysiology, using flow matching with a velocity field conditioned on the input current. On biophysically detailed models of two human cortical interneuron types, the generated responses closely reproduce the electrophysiological feature distributions, spike-time structure, and excitability profiles, even matching the experimental recordings from the corresponding human cortical neurons. Near the firing threshold, firing and non-firing responses coexist at the same stimulus amplitude, and at high amplitudes, ensembles may split into low- and high-firing modes near depolarization block. We show that our model recovers both modes in each case, while a neural operator baseline suppresses spiking near threshold and blurs the gap between modes at depolarization block.