PathFM: Fast Generative Forecasting of Multivariate Trajectories

PathFM. Fast Generative Forecasting of Multivariate Trajectories. By Jiachen Yao and seven others, from the California Institute of Technology and Amazon. Published on the fifteenth of October. No code repository is linked to it.

Time series foundation models are increasingly popular for general-purpose forecasting, but most leading models predict marginal quantiles. They describe the likely range of each future point, and leave unspecified how those points depend on one another along a path. That distinction matters for quantities that depend on the whole trajectory: cumulative demand, peak load, the timing of an event. Two forecasts can agree on every individual point and still disagree completely about how high the peak goes or when it arrives. Point scores and marginal scores do not reveal that difference, so a model can look strong on them while saying nothing about it.

PathFM is a trajectory-based forecasting model. It uses flow matching to generate complete future paths, so the dependence between time steps is part of what the model samples rather than something left out of the forecast. Each draw is one whole possible future, and the spread across many draws is where the dependence shows up.

Generating whole paths only helps if it is fast. The model is distilled down to one or two steps, and the attention cache over the history is shared across draws. Together these let PathFM produce multiple paths for a single series in roughly the time a quantile model needs to answer one query. The distilled sampler brings a second benefit: it makes it practical to optimise a calibration loss directly.

On the established forecasting benchmarks fev-bench and TIME, PathFM's marginal accuracy is competitive. To complement those evaluations, the authors introduce Forecast Path Score Bench, or fps-bench, which augments fev-bench tasks with energy and variogram scores and with downstream metrics. There, PathFM achieves a higher aggregate path score than all of the external baselines evaluated.

Experiments on chaotic systems add one more contrast. The flow model sustains long-run variability, while strong baselines rapidly collapse. In a system like that, keeping the variability alive over a long horizon is the very thing a path forecast is supposed to capture.

A quantile forecast says where each future point is likely to land. PathFM says what whole futures look like, and distillation together with cache sharing is what brings that within the cost of the simpler answer. The authors present it as making generative time series forecasting both competitive and practical, open to diverse downstream applications.