# Drift Estimation for Diffusion Processes Using Neural Networks Based on Discretely Observed Independent Paths

arXiv: https://arxiv.org/abs/2511.11161 · HTML: https://mlsanity.com/paper/2511.11161/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 15 references that are in the map.
- First posted on arXiv 14 Nov 2025.

## Builds on (most cited first, 3 of 3)

- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Learning Stochastic Differential Equations With Gaussian Processes Without Gradient Matching](https://mlsanity.com/paper/1807.05748/) (2018)

## Built on by (most cited first, 3 of 3)

- [Drift Estimation for Stochastic Differential Equations with Denoising Diffusion Models](https://mlsanity.com/paper/2602.17830/) (2026)
- [Plug-In Classification of Drift Functions in Diffusion Processes Using Neural Networks](https://mlsanity.com/paper/2602.02791/) (2026)
- [Error Bounds for a Diffusion Model-Based Drift Estimator](https://mlsanity.com/paper/2606.02115/) (2026)

## Abstract (arXiv)

This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process, based on high-frequency discrete observations from N independent trajectories. We propose a neural network-based estimator and derive a non-asymptotic convergence rate, decomposed into a training error, an approximation error, and a diffusion-related term scaling as log N/N. For compositional drift functions, we establish an explicit rate. In the numerical experiments, we consider a drift function with local fluctuations generated by a double-layer compositional structure featuring local oscillations, and show that the empirical convergence rate becomes independent of the input dimension d. Compared to the B-spline method, the neural network estimator achieves better convergence rates and more effectively captures local features, particularly in higher-dimensional settings.