Physical Fidelity Reconstruction via Improved Consistency-Distilled Flow Matching for Dynamical Systems

TL;DR

This paper introduces a method to compress high-fidelity flow-matching models into fast, one-step generative models for real-time scientific flow reconstruction, maintaining accuracy while significantly improving speed and efficiency.

Contribution

The authors propose a novel teacher-student distillation approach that creates compact, fast flow reconstruction models from high-capacity teachers, enabling real-time applications.

Findings

Distilled models retain similar spectral performance to teachers.

Achieve approximately 12x inference speedup.

Outperform directly trained one-step models by 23.1% in SSIM.

Abstract

Reconstructing high-fidelity flow fields from low-fidelity observations is a central problem in scientific machine learning, yet recent diffusion and flow-matching models typically rely on iterative sampling, making them costly for latency-sensitive workflows such as ensemble forecasting, real-time visualization, and simulation-in-the-loop inference. We study whether a high-fidelity flow-matching generative model can be compressed into a compact one-step model for fast scientific flow reconstruction. Our approach distills an optimal-transport flow-matching teacher into a one-step consistency model. Low-fidelity observations are incorporated at inference by initializing the generative trajectory from a noised observation along the transport path, allowing an unconditional high-fidelity flow model to perform conditional reconstruction without retraining the teacher. We evaluate this distillation strategy on three fluid benchmarks, Smoke Buoyancy, Turbulent Channel Flow, and Kolmogorov Flow, using coarse-to-fine reconstruction as a controlled testbed at field sizes up to $256 \times 256$. Across these settings, the distilled student retains similar performance of the teacher's model on spectrum metrics, while using roughly half as many parameters and achieving a $12\times$ inference speedup over the flow-matching teacher. Under the same training budget, the distilled student also outperforms a one-step consistency model trained directly from scratch by $23.1\%$ in SSIM, showing that teacher distillation improves training efficiency rather than merely accelerating sampling. These results suggest a promising route for turning future high-capacity scientific generative models into compact reconstruction models that are faster to train, cheaper to run, and easier to deploy.