Recursive Flow Matching
This work addresses the speed-fidelity trade-off in generative models for scientific emulation, enabling high-fidelity one- and few-step dynamic generation for physics-based tasks.
Recursive Flow Matching (RecFM) introduces a generative framework that enforces self-consistency across discretization scales to forecast complex spatiotemporal dynamics, achieving up to 20x speedup over diffusion-based emulators and over 15% reduction in mean squared error compared to vanilla flow matching.
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.