# Generative Modeling of Neural Dynamics via Latent Stochastic Differential Equations

arXiv: https://arxiv.org/abs/2412.12112 · HTML: https://mlsanity.com/paper/2412.12112/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 87 references that are in the map.
- First posted on arXiv 1 Dec 2024.

## Builds on (most cited first, 29 of 29)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Theoretical guarantees for sampling and inference in generative models with latent diffusions](https://mlsanity.com/paper/1903.01608/) (2019)
- [Coupled Oscillatory Recurrent Neural Network (coRNN): An accurate and (gradient) stable architecture for learning long time dependencies](https://mlsanity.com/paper/2010.00951/) (2020)
- [Attractor and integrator networks in the brain](https://mlsanity.com/paper/2112.03978/) (2021)
- [Neural Latents Benchmark '21: Evaluating latent variable models of neural population activity](https://mlsanity.com/paper/2109.04463/) (2021)
- [Variational Recurrent Auto-Encoders](https://mlsanity.com/paper/1412.6581/) (2014)
- [Learning identifiable and interpretable latent models of high-dimensional neural activity using pi-VAE](https://mlsanity.com/paper/2011.04798/) (2020)
- [Oscillatory State-Space Models](https://mlsanity.com/paper/2410.03943/) (2024)
- [Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Data](https://mlsanity.com/paper/2402.14989/) (2024)
- [Learning interpretable continuous-time models of latent stochastic dynamical systems](https://mlsanity.com/paper/1902.04420/) (2019)
- [Large-scale neural recordings call for new insights to link brain and behavior](https://mlsanity.com/paper/2103.14662/) (2021)
- [Trajectory Flow Matching with Applications to Clinical Time Series Modeling](https://mlsanity.com/paper/2410.21154/) (2024)
- [Identifying Latent Stochastic Differential Equations](https://mlsanity.com/paper/2007.06075/) (2020)
- [Targeted Neural Dynamical Modeling](https://mlsanity.com/paper/2110.14853/) (2021)
- [Amortized Reparametrization: Efficient and Scalable Variational Inference for Latent SDEs](https://mlsanity.com/paper/2312.10550/) (2023)
- [Latent SDEs on Homogeneous Spaces](https://mlsanity.com/paper/2306.16248/) (2023)
- [On Simplicity and Complexity in the Brave New World of Large-Scale Neuroscience](https://mlsanity.com/paper/1503.08779/) (2015)
- [Inferring stochastic low-rank recurrent neural networks from neural data](https://mlsanity.com/paper/2406.16749/) (2024)
- [Modeling Latent Neural Dynamics with Gaussian Process Switching Linear Dynamical Systems](https://mlsanity.com/paper/2408.03330/) (2024)
- [Building population models for large-scale neural recordings: opportunities and pitfalls](https://mlsanity.com/paper/2102.01807/) (2021)
- [Expressive dynamics models with nonlinear injective readouts enable reliable recovery of latent features from neural activity](https://mlsanity.com/paper/2309.06402/) (2023)
- [Universal Differential Equations as a Common Modeling Language for Neuroscience](https://mlsanity.com/paper/2403.14510/) (2024)
- [Effective Latent Differential Equation Models via Attention and Multiple Shooting](https://mlsanity.com/paper/2307.05735/) (2023)
- [Simulations Approaching Data: Cortical Slow Waves in Inferred Models of the Whole Hemisphere of Mouse](https://mlsanity.com/paper/2104.07445/) (2021)

## Built on by (most cited first, 4 of 4)

- [SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equations](https://mlsanity.com/paper/2502.02472/) (2025)
- [Generative Modeling of Clinical Time Series via Latent Stochastic Differential Equations](https://mlsanity.com/paper/2511.16427/) (2025)
- [Probabilistic Prediction of Neural Dynamics via Autoregressive Flow Matching](https://mlsanity.com/paper/2604.11178/) (2026)
- [Learning Implicit Causal World Models from Multi-Agent Demonstrations](https://mlsanity.com/paper/2607.26336/) (2026)

## Abstract (arXiv)

We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic dynamical system which implements computations through its state evolution. To model this dynamical system, we employ a system of coupled stochastic differential equations with differentiable drift and diffusion functions and use variational inference to infer its states and parameters. This formulation enables seamless integration of existing mathematical models in the literature, neural networks, or a hybrid of both to learn and compare different models. We demonstrate this in our framework by developing a generative model that combines coupled oscillators with neural networks to capture latent population dynamics from single-cell recordings. Evaluation across three neuroscience datasets spanning different species, brain regions, and behavioral tasks show that these hybrid models achieve competitive performance in predicting stimulus-evoked neural and behavioral responses compared to sophisticated black-box approaches while requiring an order of magnitude fewer parameters, providing uncertainty estimates, and offering a natural language for interpretation.