Seq-Flow: Efficient Probabilistic Forecasting with Self-Rollout Error Control

2026-10-07

AI Summary

This study addresses the high inference costs of conventional diffusion models and the error accumulation inherent in warm-start methods under few-step sampling. We propose a probabilistic forecasting framework based on conditional flow matching, which efficiently transports samples from a prior distribution to an updated distribution via ordinary differential equations. Furthermore, we introduce a novel self-rolling training mechanism that leverages a moving-average model to generate initial states, thereby suppressing error accumulation during recursive reuse. Experimental results on particle accelerator beam prediction tasks demonstrate that the proposed method reduces the Continuous Ranked Probability Score (CRPS) by 65% while maintaining high accuracy over more than 400 consecutive updates. Ultimately, this work achieves efficient and stable probabilistic forecasting suitable for real-time scientific applications.

Abstract

Many scientific forecasting tasks require updating a distribution over future trajectories as new observations arrive. Conventional diffusion and flow models generate each forecast from Gaussian noise, often at the cost of many sampling steps. Warm-start methods reuse earlier predictions to reduce this cost, but their models are not trained to perform the forecast update itself, which can compromise quality under few-step sampling. In this work, we introduce Seq-Flow, a conditional flow model whose ODE transports samples from the previous forecast distribution to the updated one. Because successive forecasts often differ only modestly, this transport starts from an informative distribution and can produce accurate updates with few flow evaluations. Recursive reuse also creates a challenge: errors in one forecast become errors in the initial states of subsequent flows. We address this with self-rollout training, in which a moving average copy of the model generates forecasts that initialize later training updates. Unlike self-forcing methods, which reuse generated outputs as conditioning context, Seq-Flow reuses them as the source of the next flow. Experiments On particle-accelerator beam spill forecasting show Seq-Flow reduces CRPS by 65% under a few-NFE sampling budget, while remaining competitive with strong baselines on fluid-dynamics forecasting tasks. Although trained on self-rollouts of at most four updates, Seq-Flow remains accurate over more than 400 consecutive updates. Our code is available at https://github.com/Graph-COM/Seq-Flow.

Problem

• probabilistic forecasting
• flow models
• error accumulation
• few-step sampling
• distribution update

Innovation

• Conditional Flow Model
• Self-Rollout Training
• Probabilistic Forecasting
• Error Control
• Few-step Sampling