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

arXiv: https://arxiv.org/abs/2610.10440 · HTML: https://mlsanity.com/paper/2610.10440/

## Key facts

- No citing papers in the map yet (data through 7 Oct 2026).
- Builds on 8 of its 48 references that are in the map.
- First posted on arXiv 7 Oct 2026.

## Builds on (most cited first, 8 of 8)

- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Autoregressive Diffusion Models](https://mlsanity.com/paper/2110.02037/) (2021)
- [Streaming Flow Policy: Simplifying diffusion/flow-matching policies by treating action trajectories as flow trajectories](https://mlsanity.com/paper/2505.21851/) (2025)
- [RealPDEBench: A Benchmark for Complex Physical Systems with Real-World Data](https://mlsanity.com/paper/2601.01829/) (2026)
- [STEP: Warm-Started Visuomotor Policies with Spatiotemporal Consistency Prediction](https://mlsanity.com/paper/2602.08245/) (2026)
- [TimeBridge: Better Diffusion Prior Design with Bridge Models for Time Series Generation](https://mlsanity.com/paper/2408.06672/) (2024)
- [ODEWorld: A Continuous Predictive Architecture via Physical-Time Flow](https://mlsanity.com/paper/2607.27924/) (2026)
- [Warm Starts Accelerate Conditional Diffusion](https://mlsanity.com/paper/2507.09212/) (2025)

## Abstract (arXiv)

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.