LIFT: Local-to-Interaction Flow Matching for Multivariate Time Series Generation

Multivariate time-series generators must reproduce both the dynamics of individual channels and the dependencies that make their trajectories jointly coherent. Several existing generators provide temporal context for cross-channel computation, but do not explicitly train the representations used for such interaction through a channel-local velocity prediction objective. We introduce LIFT, a flow-matching framework for unconditional generation that trains channel-local temporal representations and reuses the same states for multivariate refinement. A shared temporal encoder processes each channel independently, and a local head predicts its velocity using only that channel’s trajectory. An interaction module reads the resulting states and predicts an additive correction conditioned on the joint sample. The local and complete velocities are trained jointly against the same flow-matching target; under a joint realizability assumption, the ideal correction is the difference between joint and channel-local conditional velocity estimates. A mean–carrier module combines broadcast mean context with channel-specific readouts from a small set of pooled carriers, yielding computation linear in channel count at fixed width and carrier count. Across six benchmarks and eight baselines, LIFT achieves the lowest three-seed mean in 23 of 24 dataset–metric comparisons. Controlled variants further support temporally informed interaction and the reuse of locally supervised temporal states for joint refinement.