Drift Estimation for Stochastic Differential Equations with Denoising Diffusion Models

• URL: http://arxiv.org/abs/2602.17830v1
• Date: Thu, 19 Feb 2026 20:49:15 GMT
• Title: Drift Estimation for Stochastic Differential Equations with Denoising Diffusion Models
• Authors: Marcos Tapia Costa, Nikolas Kantas, George Deligiannidis,
• Abstract summary: We formulate drift estimation as a denoising problem conditional on previous observations.<n>We propose an estimator of the drift function which is a by-product of training a conditional diffusion model capable of new trajectories dynamically.<n>Across different drift classes, the proposed estimator was found to match classical methods in low dimensions and remained consistently competitive in higher dimensions.
• Score: 6.231343612183477
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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