Also known as: rectified flow, conditional flow matching, CFM, flow-based generation, stochastic interpolant
A generative-modeling objective that learns a continuous vector field transporting noise to data along straight or curved probability paths. Generalizes and often replaces diffusion: simpler training, faster sampling, and the substrate behind SD3, Flux, and Veo.
Flow matching is a generative-modeling framework that learns a continuous vector field
Pick a probability path connecting noise
The instantaneous velocity along this path is
Sample
Diffusion learns the score
Flow matching is what diffusion looks like when you stop pretending the forward process has to be stochastic. The objective is plain
The training objective is a clean
The framework is parametric in the path. Different choices yield different methods, all sharing the same regression machinery:
Diffusion’s reverse SDE has a deterministic equivalent — the probability-flow ODE — that traces the same marginal distributions at every timestep without any noise injection. That ODE is a flow-matching solution. Flow matching just trains it directly rather than going through the SDE detour and then deriving the ODE from Anderson’s theorem. The upstream stochastic-calculus machinery built on Brownian motion is unnecessary if you only want the deterministic transport — you can write down the training objective without ever invoking an SDE.
A 25-step DDPM image at 1024×1024 takes ~2-4 seconds on an A100. A 4-step rectified-flow generation at the same resolution takes ~300-500 ms. For text-to-image at production scale — millions of queries per day, billions per month — that 6-10× latency cut is the difference between flow matching being a curiosity and being the default. Black Forest Labs’ Flux Schnell variant runs in 1-4 steps and was designed explicitly around this constraint: same architecture as Flux Dev, distilled to a few-step rectified-flow regime. The economics show up at every layer of the stack — GPU utilization, batch sizing, latency budgets, end-user perceived quality.
The framework is modality-agnostic. Veo (Google’s video model), CAT3D (multi-view 3D), and Movie Gen (Meta) all train flow-matching objectives over their respective tensor spaces — temporal latents for video, multi-view latents for 3D. The vector field operates over whatever tensor shape you pick; the path interpolation generalizes uniformly because it’s just a convex combination on Euclidean space. The architectural choices around conditioning (text injection, view-pose conditioning, temporal attention) are inherited from the diffusion era largely unchanged — a typical SD3-style vision transformer (DiT) backbone with CLIP and T5 text encoders. What flow matching changes is the objective and the sampler, not the rest of the stack.
The practical upshot: in 2024-25, “we trained a diffusion model” almost always means “we trained a rectified-flow model with a DiT backbone.” The vocabulary lags the practice. The terminology will likely converge over the next 18 months on flow matching as the umbrella name, with diffusion as the historical predecessor.
Diffusion learns to predict noise (or score) along a stochastic SDE that gradually corrupts data. Flow matching learns a deterministic vector field along arbitrary probability paths — typically straight lines from noise to data. Same generative power, simpler training objective (
Straight paths (rectified flow, Liu et al. 2022) discretize with much fewer ODE steps — often 1-4 steps versus 25-50 for DDPM. The intuition: a straight path has constant velocity, so first-order Euler integration is exact in the limit of perfect velocity prediction. Curved paths force the solver to take small steps to track curvature.
Stable Diffusion 3 (rectified flow transformer), Flux (Black Forest Labs), Veo (Google), and Movie Gen (Meta). The 2024-25 shift from diffusion to flow matching was driven by the sampling-speed advantage at production scale — when you serve millions of images a day, a 10x latency cut on inference is the entire business case.
