Flow Matching

Flow Matching continuously maps a noise distribution to a data distribution by learning a deterministic velocity field, and both Stable Diffusion 3 and Flux adopt this framework.

Flow Matching was proposed by Lipman et al. in 2022 and directly learns a deterministic ODE flow that maps a noise distribution to a data distribution.

Flow matching models generate images by learning a continuous probability flow (ODE trajectory) from the noise distribution to the data distribution, and are generally more stable to train and require fewer inference steps.

Flow matching is a generative model training method that directly learns a deterministic ODE path from the noise distribution to the data distribution, defines a linear interpolation path xt=(1-t)x₀+tx₁, and uses a neural network to learn to predict the velocity vector at every point along that path.

Flux基于流匹配（Flow Matching）技术，在写实质感和光影处理上表现突出

Flow Matching was proposed by Lipman et al. in 2022, extending discrete time steps to continuous-time manifolds and replacing stochastic sampling with a deterministic ODE solver.

Veo 3基于Google的Flow Matching技术构建

The reverse SDE of a diffusion process can be expressed as dX_t = [f(X_t,t) - g(t)²∇log p_t(X_t)]dt + g(t)dW̄_t.

New-generation models such as FLUX and Z-Image, due to architectural improvements, achieve optimal results with a CFG value of 1 or even lower, whereas traditional Stable Diffusion models typically use CFG values of 7–12.

SteerTTS's optional flow-matching refiner uses a ConvNeXt backbone with 10 midpoint steps to enhance mel detail, at a cost of roughly 12x compute.

REKI uses Flow Matching to generate actions and uses 10-step Euler integration at inference time.

REKI's register tokens are constrained by an attention mask and never read action tokens, so they only need to be computed once before the Euler integration loop begins.

In the second attempt to build a joint video-action model, the team used the pretrained video prediction model Cosmos Predict 2.5-2B as the backbone network, extracting intermediate latent features during the video generation denoising process, and feeding them together with the robot's proprioceptive state and noisy action tokens into the Gemma Action Head, jointly generating denoised action control tokens through Flow Matching.

π0 introduces an action decoding head based on Flow Matching, which outputs high-frequency, continuous dexterous manipulation actions while retaining language understanding capabilities.

MeanFlow is a generative modeling paradigm based on flow matching that parameterizes the average velocity of an entire trajectory as a single network output, theoretically enabling high-quality image synthesis in a single forward inference step.

DenoFlow is a method for denoising steady-state visual evoked potential (SSVEP) EEG signals, adopting a Flow Matching modeling approach.

Rectified Flow is a specific implementation of flow matching that straightens the path between the source distribution and the target distribution into a straight line, enabling fewer integration steps and higher generation efficiency.

MintFlow is a training-free constrained sampling framework that reformulates the constraint imposition process as minimal intervention on pre-trained flow trajectories.

Compared to score-function-based diffusion models, the flow matching training objective is more concise, and the trajectory can be designed as a rectified flow, enabling high-quality generation in fewer inference steps.

Alternative training objectives such as Flow Matching have demonstrated faster convergence speeds than traditional DDPM