Flow Matching

Flow matching is a framework for training generative machine learning models in which a neural network learns a continuous vector field that transports samples from a simple distribution, such as Gaussian noise, to the target data distribution along a chosen probability path.^[1] It was introduced as an alternative to diffusion models and offers a simpler training objective, fewer required sampling steps, and more direct control over the geometry of the generative process. Since 2024 it has become the dominant training paradigm for state-of-the-art image and video generation models, including Stable Diffusion 3, FLUX, Veo, and Movie Gen.^[7]

Background

Generative models such as diffusion models learn to reverse a gradual noise-corruption process, iteratively denoising samples over hundreds of steps. While effective, this approach has two practical drawbacks: the training objective is indirect (predicting noise at random timesteps), and sampling is slow because many denoising iterations are required. Flow matching was developed to address both issues by reframing generation as the task of learning an ordinary differential equation (ODE) — a "flow" — that directly moves probability mass from noise to data.^[1][2]

The theoretical foundations were laid in 2022 by Liu, Gong, and Liu, who introduced rectified flow, a method that learns straight-line transport maps between two distributions and showed that repeatedly "rectifying" the learned trajectories produces nearly straight paths that can be sampled in one or a few steps.^[2] In 2023, Lipman et al. generalised this into conditional flow matching (CFM), which regresses a network onto conditional velocity fields defined for individual data points, making the objective both simple and scalable.^[1]

Key Concepts

The core idea of flow matching is to interpolate between a noise sample and a data sample along a path, typically a straight line: at time t, the interpolated point is a weighted combination of noise and data. The network is trained to predict the velocity — the direction and speed of movement along the path — at each interpolated point.^[1] At inference, a sample is generated by numerically integrating the learned vector field, using techniques such as the Euler method, from pure noise to the final output.

Because the conditional paths used in flow matching are designed to be nearly straight, large integration steps remain accurate, allowing high-quality generation in a small number of steps — often 1 to 4 in rectified-flow-based models — compared with the hundreds of steps used by early diffusion models.^[3][7] Flow matching also generalises diffusion: diffusion models can be viewed as a special case of flow matching on a particular noise schedule, and the two frameworks share the same underlying mathematics of probability paths and stochastic differential equations.^[1][4]

When combined with transformer backbones, flow matching scales effectively to very large models. Esser et al. (2024) demonstrated that rectified flow transformers could be scaled up to state-of-the-art image synthesis quality, forming the basis of Stable Diffusion 3.^[3]

Applications and Impact

Flow matching has been widely adopted in production generative AI systems. Stability AI's Stable Diffusion 3 (2024) replaced the U-Net denoiser of earlier models with a multimodal diffusion transformer trained using rectified flow, improving text rendering and compositional accuracy.^[3][6] Black Forest Labs' FLUX image models, Google's Veo video models, and Meta's Movie Gen are also built on flow-matching or rectified-flow architectures.^[7] The framework is also used in audio synthesis, molecule generation, and language modelling research.^[4]

The main practical impact of flow matching has been on inference cost: because models can produce outputs in one to a few steps, serving millions of generations per day becomes far cheaper, which was a decisive factor in the industry's shift from diffusion to flow matching during 2024–2025.^[7]

>See Also

• Diffusion Model
• Stable Diffusion
• Transformer Architecture
• Generative Adversarial Network
• FLUX (image generation model)

References