# Neural Stochastic Flows: Solver-Free Modelling and Inference for SDE Solutions

arXiv: https://arxiv.org/abs/2510.25769 · HTML: https://mlsanity.com/paper/2510.25769/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 58 references that are in the map.
- First posted on arXiv 29 Oct 2025.

## Builds on (most cited first, 30 of 39)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Stochastic Video Generation with a Learned Prior](https://mlsanity.com/paper/1802.07687/) (2018)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data](https://mlsanity.com/paper/1605.06432/) (2016)
- [Equinox: neural networks in JAX via callable PyTrees and filtered transformations](https://mlsanity.com/paper/2111.00254/) (2021)
- [Composing graphical models with neural networks for structured representations and fast inference](https://mlsanity.com/paper/1603.06277/) (2016)
- [Stochastic Latent Residual Video Prediction](https://mlsanity.com/paper/2002.09219/) (2020)
- [Consistency Flow Matching: Defining Straight Flows with Velocity Consistency](https://mlsanity.com/paper/2407.02398/) (2024)
- [Neural Flows: Efficient Alternative to Neural ODEs](https://mlsanity.com/paper/2110.13040/) (2021)
- [Normalizing Flows are Capable Generative Models](https://mlsanity.com/paper/2412.06329/) (2024)
- [Hierarchical Variational Models](https://mlsanity.com/paper/1511.02386/) (2015)

## Built on by (most cited first, 5 of 5)

- [Strong Stochastic Flow Maps](https://mlsanity.com/paper/2606.01086/) (2026)
- [Learning Continuous Neural Representation of Stochastic Hybrid Systems](https://mlsanity.com/paper/2609.38893/) (2026)
- [Gaussian Flow Dynamics: Simulation-Free Neural SDE Learning Beyond One-Time Marginals](https://mlsanity.com/paper/2610.04390/) (2026)
- [Langevin Flow Maps: Efficient Molecular Dynamics and Transition Path Sampling](https://mlsanity.com/paper/2610.05998/) (2026)
- [Scan-Parallel Variational Inference for event-driven Latent Jump Models](https://mlsanity.com/paper/2610.12986/) (2026)

## Abstract (arXiv)

Stochastic differential equations (SDEs) are well suited to modelling noisy and irregularly sampled time series found in finance, physics, and machine learning. Traditional approaches require costly numerical solvers to sample between arbitrary time points. We introduce Neural Stochastic Flows (NSFs) and their latent variants, which directly learn (latent) SDE transition laws using conditional normalising flows with architectural constraints that preserve properties inherited from stochastic flows. This enables one-shot sampling between arbitrary states and yields up to two orders of magnitude speed-ups at large time gaps. Experiments on synthetic SDE simulations and on real-world tracking and video data show that NSFs maintain distributional accuracy comparable to numerical approaches while dramatically reducing computation for arbitrary time-point sampling.