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

2026-05-07

AI Summary

This work addresses the challenge of efficiently reconstructing high-fidelity flow fields from low-fidelity observations by proposing a single-step consistency generative model grounded in optimal transport flow matching. The approach distills an iterative teacher model into a single-step student model and integrates a noise-initialized conditional reconstruction mechanism, enabling flexible conditional inference without retraining. Evaluated on three canonical fluid dynamics benchmarks, the method achieves a 12× acceleration in inference speed and a 50% reduction in model parameters compared to the teacher, while improving SSIM by 23.1% over a naively trained single-step baseline. Moreover, its spectral fidelity closely matches that of the teacher model, demonstrating a strong balance among reconstruction quality, computational efficiency, and generalization capability.

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.

Problem

• flow reconstruction
• low-fidelity observations
• scientific machine learning
• generative models
• inference latency

Innovation

• flow matching
• consistency distillation
• scientific machine learning
• one-step generation
• high-fidelity reconstruction