Diffusion Models for Adaptive Sequential Data Generation

2026-06-04

AI Summary

Existing diffusion models struggle to preserve causality and adaptivity when generating time series, often inadvertently incorporating future information. This work proposes a sequential forward–backward diffusion framework that relies solely on historical data for both noise injection and denoising, thereby ensuring strict temporal adaptivity. We introduce a novel conditional score matching objective that enables parallel training and, for the first time, establish a general theoretical framework with statistical guarantees, proving convergence of both score and distribution estimators. The method employs ReLU networks to model the score function, combined with a sequential noise schedule and a conditional matching strategy. Empirical validation on synthetic data—including ARMA processes and Gaussian processes—demonstrates its efficacy, and the approach is successfully applied to mean–variance optimal portfolio construction, significantly enhancing the realism and practical utility of the generated sequences.

Abstract

Generating realistic synthetic sequential data is critical in real-world applications across operations research, finance, healthcare, energy systems, and scientific computing, where time-indexed observations are used for prediction, simulation, risk assessment, and data-driven decision-making. While diffusion models have achieved remarkable success in generating static data, their direct extensions to sequential settings often fail to capture temporal dependence and information structure. Designing diffusion models that can simulate sequential data in an adapted manner, and hence without anticipation of future information, therefore remains an open challenge. In this work, we propose a sequential forward-backward diffusion framework for adapted time series generation. Our approach progressively injects and removes noise along the sequence, conditioning on the previously generated history to ensure adaptiveness. A novel score-matching objective is introduced for efficient parallel training. We derive rigorous statistical guarantees under a generic framework, then establish score approximation, score estimation, and distribution estimation results with ReLU networks serving as a concrete instance. Empirically, we validate our method on synthetic data, including ARMA models and Gaussian processes, and demonstrate its effectiveness in constructing mean-variance optimal portfolios.

Problem

• diffusion models
• sequential data generation
• temporal dependence
• adaptiveness
• time series

Innovation

• sequential diffusion models
• adapted generation
• score matching
• temporal dependence
• distribution estimation