Recursive Flow Matching

2026-05-26

AI Summary

This work addresses the longstanding challenge in physical system modeling of balancing high-fidelity generation with low computational cost. The authors propose a Recursive Flow Matching (RecFM) framework that significantly reduces discretization error by enforcing self-consistency constraints across multi-scale discrete trajectories, enabling efficient and highly accurate spatiotemporal dynamics prediction. Notably, RecFM is the first method to support high-fidelity dynamic generation in one step over multiple timesteps (2–4 steps), achieving performance comparable to state-of-the-art multi-step solvers and thereby overcoming the traditional speed–accuracy trade-off inherent in generative models. Experimental results demonstrate that RecFM accelerates inference by up to 20× compared to leading diffusion models on multiple scientific benchmarks while reducing mean squared error by over 15% relative to standard flow matching.

Abstract

Generative models have emerged as a powerful paradigm for solving physics systems and modeling complex spatiotemporal dynamics. However, achieving high physical accuracy without incurring high computational cost remains a fundamental challenge, as existing approaches face a critical speed-fidelity trade-off. In this work, we introduce Recursive Flow Matching (RecFM), a generative framework for forecasting complex spatiotemporal dynamics. RecFM enforces self-consistency to align trajectories across discretization scales, reducing discretization errors and improving performance across metrics for physics-based tasks. To our knowledge, this is the first method to achieve high-fidelity one- and few-step (2-4 step) dynamic generation for scientific systems with performance comparable to state-of-the-art multi-step solvers. Across challenging scientific benchmarks, RecFM achieves up to a 20$\times$ speedup over leading diffusion-based emulators while improving predictive accuracy. Furthermore, RecFM reduces mean squared error by over 15% compared to vanilla flow matching, offering a scalable and efficient solution for real-time scientific emulation.

Problem

• spatiotemporal dynamics
• physical accuracy
• computational cost
• speed-fidelity trade-off
• generative models

Innovation

• Recursive Flow Matching
• self-consistency
• spatiotemporal dynamics
• discretization error reduction
• scientific emulation