Title: Time-Gated Multi-Scale Flow Matching for Time-Series Imputation
Primary area: learning on time series and dynamical systems
Keywords: Time-series imputation, Flow matching, ODE-based generative models, Transformers, Multi-scale modeling

Abstract: We address multivariate time–series imputation by learning the velocity field of a
data-conditioned ordinary differential equation (ODE) via flow matching. Our
method, 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 recon-
cile 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 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 regu-
larizers for numerical stability. Across standard benchmarks, Time-Gated Multi-
Scale Flow Matching attains competitive or improved MSE/MAE with favorable
speed–quality trade-offs, and ablations isolate the contributions of the time-gated
multi-scale heads, masked attention, and the data-consistent ODE integration