Title: CL-DPS: A Contrastive Learning Approach to Blind Nonlinear Inverse Problem Solving via Diffusion Posterior Sampling
Primary area: applications to computer vision, audio, language, and other modalities
Keywords: Diffusion Models, Blind Inverse Problems, Contrastive Learning

Abstract: Diffusion models (DMs) have recently become powerful priors for solving inverse problems. However, most work focuses on non-blind settings with known measurement operators, and existing DM-based blind solvers largely assume linear measurements, which limits practical applicability where operators are frequently nonlinear. We introduce CL-DPS, a contrastively trained likelihood for diffusion posterior sampling that requires no knowledge of the operator parameters at inference. To the best of our knowledge, CL-DPS is the first DM-based framework capable of solving blind nonlinear inverse problems. Our key idea is to train an auxiliary encoder offline, using a MoCo-style contrastive objective over randomized measurement operators, to learn a surrogate for the conditional likelihood \$p(\boldsymbol{y} | \boldsymbol{x}\_t)\$. During sampling, we inject the surrogate's gradient as a guidance term along the reverse diffusion trajectory, which enables posterior sampling without estimating or inverting the forward operator. We further employ overlapping patch-wise inference to preserve fine structure and a lightweight color-consistency head to stabilize color statistics. The guidance is sampler-agnostic and pairs well with modern solvers (e.g., DPM-Solver++ (2M)). Extensive experiments show that CL-DPS effectively handles challenging nonlinear cases, such as rotational and zoom deblurring, where prior DM-based methods fail, while remaining competitive on standard linear benchmarks. Code: \url{https://anonymous.4open.science/r/CL-DPS-4F5D}.