(Maths-IA) Flow Matching Meets Denoising: A Plug-and-Play Approach to Inverse Problems

In this talk, we explore the connections between flow matching and

denoising, and show how these links can be leveraged to solve imaging

inverse problems such as super-resolution and inpainting. We begin with

a brief introduction to flow matching generative models, and recall the

classical formulation of inverse problems, along with standard non-

generative approaches, with a focus on the Plug-and-Play (PnP) framework.

We then introduce PnP-Flow, a method that bridges flow matching and PnP.

Our approach constructs a time-dependent denoiser from a pre-trained

flow matching model, and integrates it into an iterative scheme

combining data-fidelity updates, reprojections onto the flow trajectory,

and denoising steps. The resulting algorithm is efficient, memory-

friendly, and achieves strong performance across a range of inverse

problems.

The second part of the talk focuses on how to train effective generative

denoisers and provides practical guidelines. In particular, we

investigate the impact of time weighting in the loss, as well as the

parameterization of the neural network (e.g., predicting velocity,

noise, or the denoised signal). Although these formulations are

theoretically equivalent under perfect training, we show that they lead

to markedly different empirical performance.