In this tutorial post, we provide an accessible introduction to flow-matching and rectified flow models, which are increasingly at the forefront of ge

Flow With What You Know

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2024-11-14 12:30:03

In this tutorial post, we provide an accessible introduction to flow-matching and rectified flow models, which are increasingly at the forefront of generative AI applications. Typical descriptions of them are usually laden with extensive probability-math equations, which can form barriers to the dissemination and understanding of these models. Fortunately, before they were couched in probabilities, the mechanisms underlying these models were grounded in basic physics, which provides an alternative and highly accessible (yet functionally equivalent) representation of the processes involved. Let’s flow.

Flow-based generative AI models have been gaining significant traction as alternatives or improvements to traditional diffusion approaches in image and audio synthesis. These flow models excel at learning optimal trajectories for transforming probability distributions, offering a mathematically elegant framework for data generation. The approach has seen renewed momentum following Black Forest Labs’ success with their FLUX models [1] , spurring fresh interest in the theoretical foundations laid by earlier work on Rectified Flows [2] in ICLR 2023. Improvements such as [3] have even reached the level of state-of-the-art generative models for one or two-step generation.

Intuitively, these models operate akin to the fluid processes that transform the shapes of clouds in the sky. While recent expositions [4] have attempted to make these concepts more accessible through probability theory, the underlying physical principles may offer a more direct path to understanding for many readers. By returning to the basic physical picture of flows that inspired these generative models, we can build both intuition and deep understanding - insights that may even guide the development of new approaches.

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