Unconditional flow-based time series generation with equivariance-regularised latent spaces
Camilo Carvajal Reyes, Felipe Tobar
TL;DR
This work tackles unconditional time-series generation by integrating flow-based sampling in a learned latent space with an equivariance-regularised autoencoder. By fine-tuning the latent space with an equivariance loss that enforces consistency under simple transformations such as translation and amplitude scaling, the authors achieve improved generation quality while preserving the efficiency of latent-flow sampling, substantially outperforming diffusion baselines in standard metrics and enabling near real-time sample generation. The approach combines latent flow matching with an explicit equivariance bias, yielding robust latent representations that interpolate well and generalise to out-of-distribution signals. Practically, the method delivers fast generation on real-world datasets (HEPC, exchange rates, weather) and demonstrates the value of geometric inductive biases for time-series generative modelling.
Abstract
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.