PathFM Generates Full Forecast Trajectories in 1–2 Flow Matching Steps

The PathFM model does not output a set of quantiles for each point of the horizon. It generates whole future trajectories of a time series. After distillation to one or two steps, it produces several such trajectories for one series in roughly the same time that a single query to a quantile model takes. The authors also introduce a benchmark, fps-bench. On aggregate path score, PathFM beats all the external baselines tested.

What quantile models are missing

Foundation models for time series are quickly gaining popularity as a universal forecasting tool. But most leading solutions predict marginal quantiles. For each step of the horizon separately, the model gives, say, the median and the interval bounds. How values at different steps relate to one another is left out of the picture.

For many tasks, that relationship is exactly what matters. Total demand over a week, a peak load on a network, the moment an event occurs: all of these depend on the entire trajectory. Take two scenarios with identical marginal distributions. In one, deviations from the forecast accumulate step by step; in the other, they cancel each other out. Their quantiles will match, but the sum and the peak will differ. Point metrics and marginal estimates do not reveal this difference.

How PathFM works

The authors take flow matching, a generative approach related to diffusion, and apply it to entire future paths. The model samples a whole trajectory at once, so the dependence between steps is built into the output itself. Such generation is usually expensive: it needs many integration steps and many repeated passes. Here, the authors address this with two techniques.

• Distilling the model to one or two sampling steps.
• A shared attention cache over the history across different samples: the series context is processed once rather than anew for each trajectory.
• Direct optimization of a calibration loss, which the fast distilled sampler makes practical.
• A speed target: several paths for one series in a time close to a single query to a quantile model.

The calibration loss deserves a separate note. When sampling is cheap, it can be built into training, directly pulling the predicted distributions toward reality.

How it was tested

On the established benchmarks fev-bench and TIME, PathFM shows competitive marginal accuracy. The model does not lose to quantile competitors on their home turf, which the authors take as evidence that the approach is practical.

To evaluate dependencies across time, the team built Forecast Path Score Bench (fps-bench). It extends the fev-bench tasks with two trajectory metrics, energy score and variogram score, as well as downstream metrics tied to practical quantities such as cumulative demand and peak. On aggregate path score, PathFM ranks above all the external baselines in the comparison.

A separate experiment was run on chaotic systems. According to the authors, the flow model preserves long-term variability, while strong baselines quickly collapse, meaning their trajectories lose diversity. For long horizons, this is an important signal: a forecast that degenerates into a smooth line describes risk poorly.

Where this could be useful

The main candidates for application are load planning in the energy sector, inventory and demand management, data-center capacity, and any scenario where a decision depends on a sum or a maximum over the horizon. Instead of a single interval, the team gets a set of plausible scenarios and computes the quantities it needs from them directly.

There are limitations as well. The description provided contains no specific numerical results, so the size of the advantage on fps-bench and the speed on real hardware need to be checked in the paper and the code. The benchmark was created by the same authors as the model, so independent verification on your own data would be wise. A practical plan: take your own tasks that depend on the trajectory, compare a quantile model with PathFM by energy and variogram score, and then by a business metric, such as peak error or total demand error.