Data-driven generative simulation of SDEs using diffusion models

• URL: http://arxiv.org/abs/2509.08731v1
• Date: Wed, 10 Sep 2025 16:17:52 GMT
• Title: Data-driven generative simulation of SDEs using diffusion models
• Authors: Xuefeng Gao, Jiale Zha, Xun Yu Zhou,
• Abstract summary: This paper introduces a new approach to generating sample paths of unknown differential equations (SDEs) using diffusion models.<n>Given a finite set of sample paths from an SDE, we utilize conditional diffusion models to generate new, synthetic paths of the same SDE.<n>In an empirical study we leverage these synthetically generated sample paths to enhance the performance of reinforcement learning algorithms.
• Score: 6.971254219321724
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper introduces a new approach to generating sample paths of unknown stochastic differential equations (SDEs) using diffusion models, a class of generative AI models commonly employed in image and video applications. Unlike the traditional Monte Carlo methods for simulating SDEs, which require explicit specifications of the drift and diffusion coefficients, our method takes a model-free, data-driven approach. Given a finite set of sample paths from an SDE, we utilize conditional diffusion models to generate new, synthetic paths of the same SDE. To demonstrate the effectiveness of our approach, we conduct a simulation experiment to compare our method with alternative benchmark ones including neural SDEs. Furthermore, in an empirical study we leverage these synthetically generated sample paths to enhance the performance of reinforcement learning algorithms for continuous-time mean-variance portfolio selection, hinting promising applications of diffusion models in financial analysis and decision-making.

Related papers

• Expanding the Chaos: Neural Operator for Stochastic (Partial) Differential Equations [65.80144621950981]
  We build on Wiener chaos expansions (WCE) to design neural operator (NO) architectures for SPDEs and SDEs.<n>We show that WCE-based neural operators provide a practical and scalable way to learn SDE/SPDE solution operators.
  arXiv  Detail & Related papers  (2026-01-03T00:59:25Z)
• Unifying and extending Diffusion Models through PDEs for solving Inverse Problems [3.1225172236361165]
  Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML)<n>Traditionally, these models have been derived using principles of variational inference, denoising, statistical signal processing, and differential equations.<n>In this study we derive diffusion models using ideas from linear partial differential equations and demonstrate that this approach has several benefits.
  arXiv  Detail & Related papers  (2025-04-10T04:07:36Z)
• Neural SDEs as a Unified Approach to Continuous-Domain Sequence Modeling [3.8980564330208662]
  We propose a novel and intuitive approach to continuous sequence modeling.<n>Our method interprets time-series data as textitdiscrete samples from an underlying continuous dynamical system.<n>We derive a maximum principled objective and a textitsimulation-free scheme for efficient training of our Neural SDE model.
  arXiv  Detail & Related papers  (2025-01-31T03:47:22Z)
• Accelerated Diffusion Models via Speculative Sampling [89.43940130493233]
  Speculative sampling is a popular technique for accelerating inference in Large Language Models.<n>We extend speculative sampling to diffusion models, which generate samples via continuous, vector-valued Markov chains.<n>We propose various drafting strategies, including a simple and effective approach that does not require training a draft model.
  arXiv  Detail & Related papers  (2025-01-09T16:50:16Z)
• A Training-Free Conditional Diffusion Model for Learning Stochastic Dynamical Systems [10.820654486318336]
  This study introduces a training-free conditional diffusion model for learning unknown differential equations (SDEs) using data. The proposed approach addresses key challenges in computational efficiency and accuracy for modeling SDEs. The learned models exhibit significant improvements in predicting both short-term and long-term behaviors of unknown systems.
  arXiv  Detail & Related papers  (2024-10-04T03:07:36Z)
• On the Trajectory Regularity of ODE-based Diffusion Sampling [79.17334230868693]
  Diffusion-based generative models use differential equations to establish a smooth connection between a complex data distribution and a tractable prior distribution. In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models.
  arXiv  Detail & Related papers  (2024-05-18T15:59:41Z)
• Gaussian Mixture Solvers for Diffusion Models [84.83349474361204]
  We introduce a novel class of SDE-based solvers called GMS for diffusion models. Our solver outperforms numerous SDE-based solvers in terms of sample quality in image generation and stroke-based synthesis.
  arXiv  Detail & Related papers  (2023-11-02T02:05:38Z)
• A Geometric Perspective on Diffusion Models [57.27857591493788]
  We inspect the ODE-based sampling of a popular variance-exploding SDE. We establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm.
  arXiv  Detail & Related papers  (2023-05-31T15:33:16Z)
• Score-based Generative Modeling Through Backward Stochastic Differential Equations: Inversion and Generation [6.2255027793924285]
  The proposed BSDE-based diffusion model represents a novel approach to diffusion modeling, which extends the application of differential equations (SDEs) in machine learning. We demonstrate the theoretical guarantees of the model, the benefits of using Lipschitz networks for score matching, and its potential applications in various areas such as diffusion inversion, conditional diffusion, and uncertainty quantification.
  arXiv  Detail & Related papers  (2023-04-26T01:15:35Z)
• Reflected Diffusion Models [93.26107023470979]
  We present Reflected Diffusion Models, which reverse a reflected differential equation evolving on the support of the data. Our approach learns the score function through a generalized score matching loss and extends key components of standard diffusion models.
  arXiv  Detail & Related papers  (2023-04-10T17:54:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.