This content refers to a research paper titled "Follow the Mean: Reference-Guided Flow Matching". It explores a new methodology in generative models.
![Follow the Mean: Reference-Guided Flow Matching [R]](/cdn-cgi/image/width=3840,quality=75,format=webp/https://preview.redd.it/5pleq5b4861h1.png?width=140&height=91&auto=webp&s=5f80ce290c30e51700f9b9fd0f907ee56e9382b2)
This paper analyzes the role of strain and vorticity in numerical integration error for flow matching, proving that strain controls exponential error amplification while vorticity contributes linearly. It further shows that optimal transport velocity fields are irrotational, leading to second-order Euler accuracy.
This research proposes PrismFlow, a new Flow Matching method for high-quality time-series data generation. It tackles the issue of overly smoothed approximations in single vector-field estimators by introducing Koopman-inspired dynamical experts that learn residual corrections.