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

arXiv: https://arxiv.org/abs/2511.14488 · HTML: https://mlsanity.com/paper/2511.14488/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 27 of its 45 references that are in the map.
- First posted on arXiv 18 Nov 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generation](https://mlsanity.com/paper/2111.08095/) (2021)
- [Dirichlet Flow Matching with Applications to DNA Sequence Design](https://mlsanity.com/paper/2402.05841/) (2024)
- [Consistency Flow Matching: Defining Straight Flows with Velocity Consistency](https://mlsanity.com/paper/2407.02398/) (2024)
- [COT-GAN: Generating Sequential Data via Causal Optimal Transport](https://mlsanity.com/paper/2006.08571/) (2020)
- [PSA-GAN: Progressive Self Attention GANs for Synthetic Time Series](https://mlsanity.com/paper/2108.00981/) (2021)
- [On the Constrained Time-Series Generation Problem](https://mlsanity.com/paper/2307.01717/) (2023)
- [Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2410.03024/) (2024)
- [Learning from Irregularly-Sampled Time Series: A Missing Data Perspective](https://mlsanity.com/paper/2008.07599/) (2020)
- [Motion Flow Matching for Human Motion Synthesis and Editing](https://mlsanity.com/paper/2312.08895/) (2023)
- [HyperTime: Implicit Neural Representation for Time Series](https://mlsanity.com/paper/2208.05836/) (2022)
- [LAFMA: A Latent Flow Matching Model for Text-to-Audio Generation](https://mlsanity.com/paper/2406.08203/) (2024)
- [FlowTS: Time Series Generation via Rectified Flow](https://mlsanity.com/paper/2411.07506/) (2024)
- [Generative Flow Network for Listwise Recommendation](https://mlsanity.com/paper/2306.02239/) (2023)
- [Self-Supervised Learning of Time Series Representation via Diffusion Process and Imputation-Interpolation-Forecasting Mask](https://mlsanity.com/paper/2405.05959/) (2024)
- [Modeling User Retention through Generative Flow Networks](https://mlsanity.com/paper/2406.06043/) (2024)
- [FlowHFT: Imitation Learning via Flow Matching Policy for Optimal High-Frequency Trading under Diverse Market Conditions](https://mlsanity.com/paper/2505.05784/) (2025)

## Built on by (most cited first, 2 of 2)

- [StaTS: Spectral Trajectory Schedule Learning for Adaptive Time Series Forecasting with Frequency Guided Denoiser](https://mlsanity.com/paper/2603.00037/) (2026)
- [CAST: Context- and Anomaly Structure-Conditioned Time Series Anomaly Generation](https://mlsanity.com/paper/2609.27825/) (2026)

## Abstract (arXiv)

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 PAFM, a Perturbation-Aware Flow Matching 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.