A Gradient Flow Approach to Solving Inverse Problems with Latent Diffusion Models

Abstract

Solving ill-posed inverse problems requires powerful and flexible priors. We propose leveraging pretrained latent diffusion models for this task through a new training-free approach, termed Diffusion-regularized Wasserstein Gradient Flow (DWGF). Specifically, we formulate the posterior sampling problem as a Wasserstein gradient flow in the latent space of an expected negative log posterior objective, regularized by a Kullback-Leibler divergence to the diffusion prior. We demonstrate the performance of our method on standard benchmarks using StableDiffusion (Rombach et al., 2022) as the prior.

arXiv commentAccepted at the 2nd Workshop on Frontiers in Probabilistic Inference: Sampling Meets Learning, 39th Conference on Neural Information Processing Systems (NeurIPS 2025). Revision (v2): fixed likelihood objective $\mathcal{F}[\mu ]$ and its derivation; the algorithm and reported results are unchanged