mlsanityData to 7 Oct 2026

Drift Estimation for Stochastic Differential Equations with Denoising Diffusion Models

arXiv 2602.17830 ↗First posted 19 Feb 2026stat.ML cs.LGcited by 1

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

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.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 33 of its 72 references that are in the map. First posted on arXiv 19 Feb 2026.

Builds on

33 of 72 references.

Closest ancestors · 17

Same direction, newest first

  1. 2024The Disappearance of Timestep Embedding in Modern Time-Dependent Neural Networks23 May
  2. 2023Continuous-Time Functional Diffusion Processes1 Mar
  3. 2023Preconditioned Score-based Generative Models13 Feb
  4. 2023Regular Time-series Generation using SGM20 Jan
  5. 2022From Denoising Diffusions to Denoising Markov Models7 Nov
  6. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  7. 2022Fast Sampling of Diffusion Models with Exponential Integrator29 Apr
  8. 2022Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models17 Jan
  9. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  10. 2021Conditional Image Generation with Score-Based Diffusion Models26 Nov
  11. 2021Learning to Efficiently Sample from Diffusion Probabilistic Models7 Jun
  12. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
5 more
  1. 2021Gotta Go Fast When Generating Data with Score-Based Models28 May
  2. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  4. 2020Denoising Diffusion Implicit Models6 Oct
  5. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 16

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  3. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  4. 2022InstructPix2Pix: Learning to Follow Image Editing Instructionscited by 2,591
  5. 2022Video Diffusion Modelscited by 2,280
  6. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  7. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
  8. 2023Geometric Latent Diffusion Models for 3D Molecule Generationcited by 185
  9. 2023Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecastingcited by 86
  10. 2023Non-autoregressive Conditional Diffusion Models for Time Series Predictioncited by 77
  11. 2023Diffusion-based Conditional ECG Generation with Structured State Space Modelscited by 35
  12. 2019Generative Adversarial Networks for Financial Trading Strategies Fine-Tuning and Combinationcited by 22
4 more
  1. 2023Non-Parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergencecited by 4
  2. 2025Drift Estimation for Diffusion Processes Using Neural Networks Based on Discretely Observed Independent Pathscited by 3
  3. 2023Improved Performance of Stochastic Gradients with Gaussian Smoothingcited by 2
  4. 2015Efficient estimation for diffusions sampled at high frequency over a fixed time intervalcited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Error Bounds for a Diffusion Model-Based Drift Estimatorcited by 0

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  3. 2026A Tutorial on Diffusion Theory: From Differential Equations to Diffusion Models
  4. 2024Structural and Convergence Analysis of Discrete-Time Denoising Diffusion Probabilistic Models
  5. 2023To smooth a cloud or to pin it down: Guarantees and Insights on Score Matching in Denoising Diffusion Models
  6. 2026Training-free score-based diffusion for parameter-dependent stochastic dynamical systems
  7. 2024On the Trajectory Regularity of ODE-based Diffusion Sampling
  8. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusions