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 Matchings
Diffusion Meets Flow Matching: Two Sides of the Same Coin Deepmind
Diffusion models and Gaussian Flow Matching are essentially the same algorithm. They only differ in formalism, network output, and noise schedule. They are interchangeable and can produce identical sampling results. The data → noise process is the same for both methods. Diffusion: progressively adds Gaussian noise to data. Flow matching: linear interpolation between data ↔ noise. When using Gaussian noise, the processes are mathematically equivalent.
There's a misconception that diffusion → stochastic curved path, flow matching → deterministic straight path. In reality, DDIM sampler (diffusion) and Euler sampler (flow matching) → produce exactly the same update equations. . Both ultimately use MSE-based loss. The difference is in what the model predicts: diffusion predicts noise or data x velocity , while flow matching predicts vector field (velocity).
In other words, diffusion → SDE (stochastic differential equation), flow matching → ODE (deterministic vector field). However, the two systems correspond to each other through parameter transformation. The difference is not fundamental, but rather in network output parameterization and noise schedule selection.
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