Generative Modeling via Flow Matching

Generative models with neural network approximations have shown impressive
results in many applications, in particular in inverse problems and data
assimilation.
Among these models, flow matching techniques stand
out for their simple applicability and good scaling properties.
We give an introduction into flow matching and show
some results of our group in this direction, namely
i) an extension to generator matching of Markov processes to learn time
series,
ii) an incorporation of flow matching into plug-and-play algorithms to
solve image restoration problems
iii) conditional flow matching using conditional Wasserstein distances,
where ii) and iii) were designed to solve image restoration problems.