CL-DPS: A Contrastive Learning Approach to Blind Nonlinear Inverse Problem Solving via Diffusion Posterior Sampling

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}.