Towards Stable and Structured Time Series Generation with Perturbation-Aware Flow Matching

TL;DR

This work tackles the challenge of generating structurally coherent time series in the presence of localized perturbations by introducing Perturbation-Aware Flow Matching (PAFM). It couples a dual-path velocity field with a Trajectory Perturbation Block and a Flow Routing Mixture-of-Experts decoder to refine velocity predictions in regions of abrupt change, guided by perturbation-induced responses. The approach yields superior performance on both unconditional and conditional generation tasks, as demonstrated through extensive experiments and ablations across real and synthetic datasets. By explicitly modeling perturbations and structural heterogeneity, PAFM improves trajectory alignment, stability, and fidelity, offering a practical framework for robust time-series synthesis in dynamic environments.

Abstract

Time series generation is critical for a wide range of applications, which greatly supports downstream analytical and decision-making tasks. However, the inherent temporal heterogeneous induced by localized perturbations present significant challenges for generating structurally consistent time series. While flow matching provides a promising paradigm by modeling temporal dynamics through trajectory-level supervision, it fails to adequately capture abrupt transitions in perturbed time series, as the use of globally shared parameters constrains the velocity field to a unified representation. To address these limitations, we introduce \textbf{PAFM}, a \textbf{P}erturbation-\textbf{A}ware \textbf{F}low \textbf{M}atching framework that models perturbed trajectories to ensure stable and structurally consistent time series generation. The framework incorporates perturbation-guided training to simulate localized disturbances and leverages a dual-path velocity field to capture trajectory deviations under perturbation, enabling refined modeling of perturbed behavior to enhance the structural coherence. In order to further improve sensitivity to trajectory perturbations while enhancing expressiveness, a mixture-of-experts decoder with flow routing dynamically allocates modeling capacity in response to different trajectory dynamics. Extensive experiments on both unconditional and conditional generation tasks demonstrate that PAFM consistently outperforms strong baselines. Code is available at https://anonymous.4open.science/r/PAFM-03B2.

Figures (12)

• Figure 1: Time series are inherently heterogeneous, as localized perturbations and abrupt shifts disrupt structural temporal continuity and hinder stable generation.
• Figure 2: Comparison between standard Flow Matching (left) and our PAFM framework (right). Standard FM fails to account for localized perturbations, resulting in misaligned or structurally inconsistent trajectories. In contrast, PAFM employs a dual-path design that integrates perturbation-guided refinement and a structure-aware decoder to adapt the velocity field, enabling temporally coherent and structurally consistent generation.
• Figure 3: Overview of the proposed perturbation-aware flow framework. (1) Trajectory Perturbation Block, consisting of Trajectory Simulation Module and Velocity Refinement Module, introduces localized perturbations to simulate abrupt disturbances and leverages dynamic feedback to refine the velocity field; (2) Velocity Field with dual-path models perturbation-aware dynamics; (3) Trajectory Decoder Block incorporates the Flow Routing Mixture-of-Experts (FRM) for structural representation.
• Figure 4: Prediction performance under different perturbation magnitudes.
• Figure 5: Imputation performance under different perturbation magnitudes.