# FlowTS: Time Series Generation via Rectified Flow

arXiv: https://arxiv.org/abs/2411.07506 · HTML: https://mlsanity.com/paper/2411.07506/

## Key facts

- Cited by 22 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 36 references that are in the map.
- First posted on arXiv 12 Nov 2024.

## 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)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Vision Transformers Need Registers](https://mlsanity.com/paper/2309.16588/) (2023)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Is Q-learning Provably Efficient?](https://mlsanity.com/paper/1807.03765/) (2018)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [Matcha-TTS: A fast TTS architecture with conditional flow matching](https://mlsanity.com/paper/2309.03199/) (2023)
- [TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generation](https://mlsanity.com/paper/2111.08095/) (2021)
- [A Tutorial on Principal Component Analysis](https://mlsanity.com/paper/1404.1100/) (2014)
- [AlphaFold Meets Flow Matching for Generating Protein Ensembles](https://mlsanity.com/paper/2402.04845/) (2024)
- [Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2307.11494/) (2023)
- [Non-autoregressive Conditional Diffusion Models for Time Series Prediction](https://mlsanity.com/paper/2306.05043/) (2023)
- [COT-GAN: Generating Sequential Data via Causal Optimal Transport](https://mlsanity.com/paper/2006.08571/) (2020)
- [Fast Point Cloud Generation with Straight Flows](https://mlsanity.com/paper/2212.01747/) (2022)
- [Motion Flow Matching for Human Motion Synthesis and Editing](https://mlsanity.com/paper/2312.08895/) (2023)
- [Regular Time-series Generation using SGM](https://mlsanity.com/paper/2301.08518/) (2023)

## Built on by (most cited first, 22 of 22)

- [TimePre: Bridging Accuracy, Efficiency, and Stability in Probabilistic Time-Series Forecasting](https://mlsanity.com/paper/2511.18539/) (2025)
- [Is Flow Matching Just Trajectory Replay for Sequential Data?](https://mlsanity.com/paper/2602.08318/) (2026)
- [SDFlow: Similarity-Driven Flow Matching for Time Series Generation](https://mlsanity.com/paper/2605.05736/) (2026)
- [Towards Stable and Structured Time Series Generation with Perturbation-Aware Flow Matching](https://mlsanity.com/paper/2511.14488/) (2025)
- [Sharpen Your Flow: Sharpness-Aware Sampling for Flow Matching](https://mlsanity.com/paper/2605.11547/) (2026)
- [WavTTS: Towards High-Quality Zero-Shot TTS via Direct Raw Waveform Modeling](https://mlsanity.com/paper/2606.03455/) (2026)
- [Enhancing Irregular Time Series Forecasting with Continuous-Time Modeling Framework](https://mlsanity.com/paper/2607.28035/) (2026)
- [Conditionally Whitened Generative Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2509.20928/) (2025)
- [Unconditional flow-based time series generation with equivariance-regularised latent spaces](https://mlsanity.com/paper/2601.22848/) (2026)
- [CoGenCast: A Coupled Autoregressive-Flow Generative Framework for Time Series Forecasting](https://mlsanity.com/paper/2602.03564/) (2026)
- [Fast Flow Matching based Conditional Independence Tests for Causal Discovery](https://mlsanity.com/paper/2602.08315/) (2026)
- [Probabilistic Prediction of Neural Dynamics via Autoregressive Flow Matching](https://mlsanity.com/paper/2604.11178/) (2026)
- [GenAI-FDIA: Physics-Informed Generative Models for False Data Injection Attacks](https://mlsanity.com/paper/2605.18873/) (2026)
- [SRT: Super-Resolution for Time Series via Disentangled Rectified Flow](https://mlsanity.com/paper/2606.07605/) (2026)
- [GALA: Generation-Aware Cross-Modal Alignment for Text-to-Time-Series Synthesis](https://mlsanity.com/paper/2608.13741/) (2026)
- [CAST: Context- and Anomaly Structure-Conditioned Time Series Anomaly Generation](https://mlsanity.com/paper/2609.27825/) (2026)
- [ChronoFlow: Hierarchical Flow Matching for Irregular Time Series Generation](https://mlsanity.com/paper/2609.33276/) (2026)
- [Supervision Recovery for Time Series Anomaly Detection via Context-Anchored Pairing](https://mlsanity.com/paper/2609.33610/) (2026)
- [FAST-Brain: A Flow-Aligned Spatio-Temporal Surrogate Brain Model](https://mlsanity.com/paper/2609.34354/) (2026)
- [KiT: A Foundation Model for Financial Time-Series Forecasting using DiffusionTransformers](https://mlsanity.com/paper/2609.34507/) (2026)
- [XMatch: Enhancing Covariate-Aware Time Series Forecasting through Tree-Structured Exogenous Matching](https://mlsanity.com/paper/2609.34939/) (2026)
- [Wavelet Flow Matching for Time Series](https://mlsanity.com/paper/2609.39374/) (2026)

## Abstract (arXiv)

Diffusion-based models have significant achievements in time series generation but suffer from inefficient computation: solving high-dimensional ODEs/SDEs via iterative numerical solvers demands hundreds to thousands of drift function evaluations per sample, incurring prohibitive costs. To resolve this, we propose FlowTS, an ODE-based model that leverages rectified flow with straight-line transport in probability space. By learning geodesic paths between distributions, FlowTS achieves computational efficiency through exact linear trajectory simulation, accelerating training and generation while improving performances. We further introduce an adaptive sampling strategy inspired by the exploration-exploitation trade-off, balancing noise adaptation and precision. Notably, FlowTS enables seamless adaptation from unconditional to conditional generation without retraining, ensuring efficient real-world deployment. Also, to enhance generation authenticity, FlowTS integrates trend and seasonality decomposition, attention registers (for global context aggregation), and Rotary Position Embedding (RoPE) (for position information). For unconditional setting, extensive experiments demonstrate that FlowTS achieves state-of-the-art performance, with context FID scores of 0.019 and 0.011 on Stock and ETTh datasets (prev. best: 0.067, 0.061). For conditional setting, we have achieved superior performance in solar forecasting (MSE 213, prev. best: 375) and MuJoCo imputation tasks (MSE 7e-5, prev. best 2.7e-4). The code is available at https://github.com/UNITES-Lab/FlowTS.