Flow-based models have proven successful for time-series generation, particularly when defined in lower-dimensional latent spaces that enable efficient sampling. However, how to design latent representations with desirable equivariance properties for time-series generative modelling remains underexplored. In this work, we propose a latent flow-matching framework in which equivariance is explicitly encouraged through a simple regularisation of a pre-trained autoencoder. Specifically, we introduce an equivariance loss that enforces consistency between transformed signals and their reconstructions, and use it to fine-tune latent spaces with respect to basic time-series transformations such as translation and amplitude scaling. We show that these equivariance-regularised latent spaces improve generation quality while preserving the computational advantages of latent flow models. Experiments on multiple real-world datasets demonstrate that our approach consistently outperforms existing diffusion-based baselines in standard time-series generation metrics, while achieving orders-of-magnitude faster sampling. These results highlight the practical benefits of incorporating geometric inductive biases into latent generative models for time series.

翻译：基于流的模型在时间序列生成方面已证明是成功的，尤其是在定义于低维潜在空间时，能够实现高效采样。然而，如何为时间序列生成建模设计具有理想等变性性质的潜在表示仍然探索不足。在本工作中，我们提出了一种潜在流匹配框架，其中通过一个预训练自编码器的简单正则化来显式鼓励等变性。具体而言，我们引入了一种等变性损失，用于强制变换后的信号与其重建之间的一致性，并利用该损失针对基本的时间序列变换（如平移和幅度缩放）对潜在空间进行微调。我们证明，这些经过等变性正则化的潜在空间在保持潜在流模型计算优势的同时，提高了生成质量。在多个真实世界数据集上的实验表明，我们的方法在标准时间序列生成指标上持续优于现有的基于扩散的基线，同时实现了数量级更快的采样速度。这些结果突显了将几何归纳偏置纳入时间序列潜在生成模型的实际益处。