PnP-CF improves solving complex inverse problems with deep generative models
PnP-CF: A Consensus Flow-Matching Solver for General Inverse Problems
Machine Learning
Summary
Inverse problems involve figuring out the cause from an observed effect, which can be tricky especially with complex or unknown systems. This paper studies a method called PnP-CF that uses learned deep models to guide the solution process, helping to find more accurate answers. The authors show that their approach works well not only for standard problems but also where the relationship between cause and effect is nonlinear or modeled by neural networks. Their method combines mathematical updates with probabilistic flow techniques to keep the solution stable and reliable.
What this means in practice
- •For image reconstruction engineers: Improve image reconstruction accuracy when the underlying process is nonlinear or partially unknown using PnP-CF with pretrained neural operators.
- •For medical device developers: Enable advanced medical imaging systems to better recover internal structures by solving nonlinear inverse problems more reliably.
Authors
Dibyanshu Kumar, Magda Gregorova
Abstract
Plug-and-Play (PnP) methods using continuous-time deep generative models as learned data distribution priors enable synthesizing high-quality solutions of model-based inverse problems. The quality of the solutions depends critically on the interplay and consensus between the inverse problem solver and the generative model sampler. We revisit a recently introduced flow-based PnP framework, which we refer to as PnP-CF (Consensus Flow), and extend its application to nonlinear inverse problems, including those with learned neural-network forward operators. PnP-CF combines a flow-matching denoiser with (i) ADMM-like dual variable updates and (ii) a time-adaptive pullback onto the intermediate flow probability path that combines a stochastic and a deterministic component. We discuss how these two features stabilize the algorithm and promote consensus, and demonstrate on a set of experiments that PnP-CF not only solves standard linear inverse problems with quality at least comparable to state-of-the-art baselines, but also extends gracefully to nonlinear inverse problems, including forward operators realized by pretrained neural networks, for which existing methods produce unsatisfactory results or fail completely.