# Time series generation with spectrally aligned latent flow matching

arXiv: https://arxiv.org/abs/2609.21989 · HTML: https://mlsanity.com/paper/2609.21989/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 34 of its 61 references that are in the map.
- First posted on arXiv 18 Sep 2026.

## 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, 30 of 34)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Vector-quantized Image Modeling with Improved VQGAN](https://mlsanity.com/paper/2110.04627/) (2021)
- [TS2Vec: Towards Universal Representation of Time Series](https://mlsanity.com/paper/2106.10466/) (2021)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Self-Supervised Contrastive Pre-Training For Time Series via Time-Frequency Consistency](https://mlsanity.com/paper/2206.08496/) (2022)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [Flow Matching in Latent Space](https://mlsanity.com/paper/2307.08698/) (2023)
- [Sobolev Training for Neural Networks](https://mlsanity.com/paper/1706.04859/) (2017)
- [Deep Signature Transforms](https://mlsanity.com/paper/1905.08494/) (2019)
- [Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU](https://mlsanity.com/paper/2001.00706/) (2020)
- [Utilizing Image Transforms and Diffusion Models for Generative Modeling of Short and Long Time Series](https://mlsanity.com/paper/2410.19538/) (2024)
- [Kernel Distribution Embeddings: Universal Kernels, Characteristic Kernels and Kernel Metrics on Distributions](https://mlsanity.com/paper/1604.05251/) (2016)
- [Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusion](https://mlsanity.com/paper/2211.02590/) (2022)
- [Time Series Diffusion in the Frequency Domain](https://mlsanity.com/paper/2402.05933/) (2024)
- [An Introduction to Flow Matching and Diffusion Models](https://mlsanity.com/paper/2506.02070/) (2025)
- [Mitigating Spectral Bias in Neural Operators via High-Frequency Scaling for Physical Systems](https://mlsanity.com/paper/2503.13695/) (2025)
- [Universal Time-Series Representation Learning: A Survey](https://mlsanity.com/paper/2401.03717/) (2024)
- [Regular Time-series Generation using SGM](https://mlsanity.com/paper/2301.08518/) (2023)
- [Lecture notes on rough paths and applications to machine learning](https://mlsanity.com/paper/2404.06583/) (2024)

## Abstract (arXiv)

Latent flow models have proven to be a reliable and cost-effective method for time series generation. However, the latent compression induces unwanted artefacts, such as a spectral mismatch with respect to the underlying dataset, thus hindering their use as training surrogates. In this article, we propose a spectrally-aligned latent-flow time series generator, where the latent space for flow matching is trained to preserve dynamical properties that are relevant for the suitability of synthetic samples. We find that incorporating fine-tuning losses based on canonical signal representations such as the Fourier, wavelet and signature transforms helps overcome these issues. The interpretability of these transformations allows us to ensure that the synthetic signals are aligned with the true ones in terms of relevant features, such as smoothness or targeted spectral content, as opposed to relying on pointwise reconstruction losses only. We compare the proposed aligned models against a base latent-flow model and the state of the art over real-world long-range univariate and multivariate benchmark datasets. Our quantitative results validate the superiority of the proposed method in terms of its performance on metrics reflecting signal realness and computational efficiency, while being aligned to the training set with respect to its local structure.