Seonglae ChoFlow Matching (FM) is a training objective (loss/formulation), not a model architecture.
Presents a method to train CNF without simulation, training the model by regressing the Vector Field of fixed conditional probability paths. The path is generally expressed as a probability flow (Vector Field) that varies with time .
This approach improves upon the sampling efficiency issues present in existing diffusion models and enables a more efficient generation process by utilizing diverse probability paths.
Flow Matching with ODE → "following a map and driving in a consistent direction" while Diffusion Model with SDE → "following a map, but random wind blows at each segment". Solver: the rule that determines how often and how precisely to apply steering in reverse direction (deterministic for ODE, stochastic for SDE). Note that diffusion models can also be sampled using ODE solvers (e.g., probability flow ODE).
Flow Matchings
Diffusion Meets Flow Matching: Two Sides of the Same Coin
Diffusion Meets Flow Matching
Flow matching and diffusion models are two popular frameworks in generative modeling. Despite seeming similar, there is some confusion in the community about their exact connection. In this post, we aim to clear up this confusion and show that <i>diffusion models and Gaussian flow matching are the same</i>, although different model specifications can lead to different network outputs and sampling schedules. This is great news, it means you can use the two frameworks interchangeably.
https://diffusionflow.github.io/
arxiv.org
https://arxiv.org/pdf/2210.02747
arxiv.org
https://arxiv.org/pdf/2412.06264
flow-GRPO flow_grpoyifan123 • Updated 2026 Mar 9 10:3, NeurIPS 2025
flow_grpo
yifan123 • Updated 2026 Mar 9 10:3
Flow Matching is ODE-based, making it deterministic (lacking sample diversity), while RL requires stochastic exploration. Additionally, RL data collection is expensive (many denoising steps), making it inefficient. By replacing the ODE sampler with an SDE that maintains the same marginal distribution, noise is injected (enabling exploration). This makes the policy at each step Gaussian, allowing to be calculated in closed form.
During RL training, even with significantly reduced denoising steps (e.g., T=10), the reward signal is sufficient for effective learning. At inference time, the original steps (e.g., T=40) are restored to maintain final quality → reducing sampling cost by 4×+. SD3.5-M improved significantly on GenEval from 63% → 95%, and text rendering from 59% → 92%. Adding KL regularization suppresses AI Reward Hacking (quality/diversity collapse) while maintaining performance gains.
arxiv.org
https://arxiv.org/pdf/2505.05470