Time-Gated Multi-Scale Flow Matching for Time-Series Imputation

We propose to perform multivariate time-series imputation by learning the velocity field of a data-conditioned ordinary differential equation (ODE) via flow matching (FM). Our method, called Time-Gated Multi-Scale Flow Matching (TG-MSFM), conditions the flow on a structured endpoint comprising observed values, a per-time visibility mask, and short left/right context, processed by a time-aware Transformer whose self-attention is masked to aggregate only from observed timestamps. To reconcile global trends with local details along the trajectory, we introduce time-gated multi-scale velocity heads on a fixed 1D pyramid and blend them through a time-dependent gate; a mild anti-aliasing filter stabilizes the finest branch. At inference, we use a second-order Heun integrator with a per-step data-consistency (DC) projection that keeps observed coordinates exactly on the straight path from the initial noise to the endpoint, reducing boundary artifacts and drift. Training adopts gap-only supervision of the velocity on missing data coordinates, with small optional regularizers for numerical stability. Across standard benchmarks, TG-MSFM attains competitive or improved performance with favorable speed-quality trade-offs, and ablations demonstrate the isolated contributions of the time-gated multi-scale heads, masked attention, and the data-consistent ODE integration. RELATED WORK Time-series imputation with deep models. Early neural approaches address missingness by designing recurrent architectures and decay mechanisms to handle irregular observations (e.g., GRU-D and BRITS). More recent encoder-decoder designs rely on self-attention to aggregate long-range temporal context. Representative non-generative baselines in our study include Transformer variants and strong forecasting models that are often adapted to imputation, such as DLinear, TimesNet,