PathFM: Fast Generative Forecasting of Multivariate Trajectories

Time series foundation models (TSFMs) are a hot topic for general-purpose forecasting, but most leading models predict marginal quantiles, leaving the dependence structure of future trajectories unspecified. This distinction matters for trajectory-dependent quantities such as cumulative demand, peak load, and event timing, yet point and marginal scores do not reveal it. To model this dependence, we introduce PathFM, a trajectory-based forecasting model that uses flow matching to generate complete future paths. We further distill the model to one or two steps and share history attention cache across draws. Together, these enable PathFM to generate multiple paths for a single series in roughly the time needed for one query to a quantile model. The distilled sampler also makes it practical to optimize a calibration loss directly. PathFM achieves competitive marginal accuracy on the established forecasting benchmarks fev-bench and TIME. To complement these evaluations, we introduce Forecast Path Score Bench (fps-bench), which augments fev-bench tasks with energy and variogram scores and downstream metrics. PathFM achieves a higher aggregate path score on fps-bench than all evaluated external baselines. Experiments on chaotic systems further show that our flow model sustains long-run variability, while strong baselines rapidly collapse. PathFM makes generative time series forecasting both competitive and practical, enabling diverse downstream applications.

From marginal quantiles to complete trajectories

Time series foundation models (TSFMs) have become increasingly popular for general-purpose forecasting. The field grows fast: every year, new models refresh the leaderboard. These models are commonly evaluated through point accuracy — mean absolute scaled error, say — and marginal probabilistic scores such as CRPS, the continuous ranked probability score. Consequently, most recent TSFMs are designed and trained to produce quantile levels, optimized for these benchmarks.

Point accuracy and marginal probabilistic scores are widely adopted for good reason: they provide an interpretable, per-step summary of forecast quality that directly supports operational decisions such as inventory planning, resource allocation, and risk management. However, they do not capture all aspects of forecast quality. Other properties, particularly trajectory-dependent ones, are important but overlooked by these metrics. Two illustrative gaps appear repeatedly:

• Learning distributions with multiple modes: Quantiles are defined through the inverse of the cumulative distribution function (CDF) of the target distribution. These CDFs are not always nice and smooth, for instance when the target distribution has multiple modes or sharp peaks. With a few or a few dozens of quantiles, the resulting approximation of the CDF can be quite rough and suffer from a regression-to-the-mean issue.
• Learning autocorrelation: Many quantile regression models predict marginal quantiles at individual time steps across a forecast window. These marginal outputs do not specify temporal dependence among future values within that window. For instance, many forecasting problems require learning trajectory-dependent quantities such as cumulative demand, peak load, and threshold-crossing times. A marginal quantile loss does not identify these joint properties.

Ad hoc methods have been proposed to mitigate these weaknesses, such as completing marginal quantiles under independence or comonotone assumptions, or learning copula structures on top of marginal forecasts. On the other hand, diffusion- or flow-matching-based generative time-series models are naturally well-suited for capturing joint trajectory distributions even without these ad hoc methods, as they can generate complete future paths while maintaining temporal and cross-variable dependencies. Unfortunately, existing generative models achieve neither high marginal accuracy nor efficient sampling, limiting their practical utility in real-world forecasting scenarios. This leads to the question: can we construct a generative time-series model that achieves both high marginal accuracy and efficient sampling while also preserving trajectory dependence?

PathFM: joint flow matching, distillation, and calibration

PathFM combines four ingredients to address the gap. First, it learns a flow over complete future trajectories through conditional flow matching, generating full multivariate paths conditioned on history and known future covariates. Second, parallel decoding distillation (PDD) groups consecutive flow-time intervals into blocks, predicting all interval velocities in a block from one backbone evaluation. The student is initialized from a frozen teacher and trained with PDD supervision alongside a fair continuous ranked probability score (CRPS) calibration loss. Third, history attention is cached once and reused across draws: the first few blocks run once per history and horizon, and their outputs are shared across paths and flow evaluations, reducing compute without sacrificing the covariates that enter through future placeholders. Fourth, the distilled sampler with one or two evaluations makes calibration gradients practical to compute, allowing the forecast distribution to be refined directly by fair CRPS.

With these components, PathFM-300M ranks second on the widely used fev-bench for marginal scores, and on Forecast Path Score Bench (fps-bench), which the authors curate to evaluate path distributions from time series foundation models on real-world data, PathFM ranks first for path scores. Both model sizes — 126M and 300M — outperform leading baselines including TimesFM-3 and Chronos-2 on fps-bench even when each quantile baseline uses its better independent or comonotone completion. On fps-bench, PathFM also improves on Sundial's native sampled forecasts across all three benchmarks. TimesFM-3 leads both marginal benchmarks, but its lower FPS ranking illustrates why marginal accuracy alone is insufficient to assess forecast paths. The clearest gains over TimesFM-3 occur in scores for temporal changes, horizon totals, and maxima, highlighting the value of complete paths for downstream tasks that depend on temporal structure beyond marginal forecasts.

Chaotic dynamics and long-run variability

Chaotic systems pose a sharp test of forecasting: can a model preserve statistical structure after losing alignment with a particular future? PathFM is evaluated on 135 DYSTS chaotic systems alongside fine-tuned Chronos-2 and PANDA, a state-of-the-art pretrained forecast model. Using sMAPE as the pointwise error metric, forecasts are assessed at horizons 64, 128, 256, and 512. Four complementary diagnostics assess dynamical fidelity: Wasserstein-1 distance to an empirical approximation of the invariant distribution, correlation-dimension error, squared Hellinger distance between normalized power spectral densities, and segment analog score. Together, these assess state occupancy, geometric dimension, frequency content, and similarity of short multivariate segments to reference dynamics.

PathFM achieves substantially better dynamical fidelity over 4,096-step rollouts than all evaluated baselines. Relative to PANDA, it reduces the four long-term diagnostic scores by 49–69%. These gains accompany the lowest pointwise error at every reported horizon and persist when PathFM is scaled down to approximately PANDA's 72M parameter count. Chronos-1 FT, an autoregressive model, achieves lower W1W1 and PSD Hellinger distance than the quantile model Chronos-2, with higher pointwise, correlation-dimension, and segment analog errors — highlighting the distinct strengths and weaknesses of traditional autoregressive and quantile forecasting models. PathFM improves across every reported metric, combining stronger point accuracy with greater dynamical fidelity.

Distillation increases point-forecast error relative to the ten-step sampler, as sensitivity to perturbations amplifies small distillation errors during autoregressive forecasts. With one or two distilled steps, PathFM still outperforms PANDA on point accuracy and all four dynamical diagnostics. Long continuations visually confirm the quantitative results: a sampled Lorenz path retains a two-lobe portrait and sustained variability, whereas baselines collapse within 256 steps. For the Halvorsen system, PathFM's sample retains the broad three-loop form, while PANDA follows a smaller recurrent orbit.

What it means in practice

For a working developer, PathFM offers a way to generate complete future trajectories from time series data without sacrificing marginal accuracy. The model's key practical contributions are: distillation enables one- or two-step generation, making ensemble forecasting as cheap as a single quantile-model query; history attention caching across paths reduces compute; and the fair CRPS calibration loss narrows the marginal accuracy gap while directly optimizing a proper scoring rule. The fps-bench benchmark, which the authors introduce, reveals how strong marginal accuracy in existing models can mask errors in temporal dependence and uncertainty over trajectory-dependent quantities — a valuable diagnostic for any organization building or selecting foundation models for forecasting. On chaotic systems, PathFM's independently continued paths preserve variability that point forecasts can lose, a property that matters for applications such as risk assessment and threshold monitoring where long-run statistical structure matters as much as short-term accuracy. A practitioner interested in integrating PathFM would need a transformer backbone with conditional flow matching, PDD distillation heads, and a calibration head that backpropagates fair CRPS through one fused sampling step; from there, the shared-history computation and stratified Gaussian noise draws are the main implementation additions.