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[2602.17830] Drift Estimation for Stochastic Differential Equations with Denoising Diffusion Models
Summary
This paper explores drift estimation in multivariate stochastic differential equations using denoising diffusion models, proposing a new estimator that performs competitively across dimensions.
Why It Matters
Understanding drift estimation in stochastic differential equations is crucial for various applications in finance, physics, and engineering. This research enhances existing methodologies by integrating advanced machine learning techniques, potentially leading to more accurate models in complex systems.
Key Takeaways
- Proposes a novel estimator for drift functions in stochastic differential equations.
- Utilizes denoising diffusion models to improve estimation accuracy.
- Demonstrates competitive performance against classical methods in both low and high dimensions.
- Highlights the importance of high-frequency data for accurate drift estimation.
- Suggests potential applications in various fields requiring stochastic modeling.
Statistics > Machine Learning arXiv:2602.17830 (stat) [Submitted on 19 Feb 2026] Title:Drift Estimation for Stochastic Differential Equations with Denoising Diffusion Models Authors:Marcos Tapia Costa, Nikolas Kantas, George Deligiannidis View a PDF of the paper titled Drift Estimation for Stochastic Differential Equations with Denoising Diffusion Models, by Marcos Tapia Costa and 2 other authors View PDF HTML (experimental) Abstract:We study the estimation of time-homogeneous drift functions in multivariate stochastic differential equations with known diffusion coefficient, from multiple trajectories observed at high frequency over a fixed time horizon. We formulate drift estimation as a denoising problem conditional on previous observations, and propose an estimator of the drift function which is a by-product of training a conditional diffusion model capable of simulating new trajectories dynamically. Across different drift classes, the proposed estimator was found to match classical methods in low dimensions and remained consistently competitive in higher dimensions, with gains that cannot be attributed to architectural design choices alone. Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG) Cite as: arXiv:2602.17830 [stat.ML] (or arXiv:2602.17830v1 [stat.ML] for this version) https://doi.org/10.48550/arXiv.2602.17830 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Marcos Tapia Costa [view email] [v1] Thu...
