Pseudoinverse-guided diffusion models are generative frameworks that solve inverse problems by directing a pretrained, problem-agnostic diffusion model toward measurement consistency using a pseudoinverse-based guidance term during the reverse sampling process. Instead of training separate models for specific reconstruction tasks, this approach leverages the unconditional score function of a general diffusion prior and incorporates the generalized or Moore-Penrose pseudoinverse of the forward measurement operator to approximate conditional scores at each denoising step. This enables zero-shot reconstruction across diverse image restoration and signal recovery tasks, accommodating noisy, linear, non-linear, and non-differentiable observation processes without requiring task-specific model retraining.
