A Geometry-Aware Metric for Mode Collapse in Multivariate Time Series Generative Models
Yassine ABBAHADDOU, Amine Aboussalah
Generative models such as Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), and diffusion models often fail to capture the full diversity of their training data, leading to mode collapse. While this issue is well-explored in image generation, it remains underinvestigated for time series data. We introduce a new definition of mode collapse specific to time series and propose a new geometry-aware metric, DMD-GEN, to quantify its severity. Our metric leverages Dynamic Mode Decomposition (DMD), a data-driven technique for identifying coherent spatiotemporal patterns through spectral analysis, and employs optimal transport between DMD eigenvectors to assess discrepancies in the underlying dynamics of the original and generated data. The geometry-aware nature of our method comes from modeling DMD modes as points on a Grassmann manifold and comparing them using Wasserstein distances computed via principal angles. When using mini-batch evaluation, DMD-GEN compares the subspaces spanned by the dominant modes of original and generated time series through optimal transport of their corresponding subspaces, enabling a principled geometric comparison. DMD-GEN is efficient in practice: it is used only during evaluation, supports mini-batch approximations, and is highly parallelizable. It not only quantifies the preservation of essential dynamic characteristics but also provides interpretability by highlighting which modes are poorly captured in the generated data. We validate DMD-GEN on both synthetic and real-world datasets using TimeGAN, TimeVAE, and DiffusionTS. The results show that DMD-GEN aligns well with traditional metrics while, for the first time, offering a principled definition of mode collapse for time series.