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 regularized Wasserstein gradient flow of the Kullback-Leibler divergence in the latent space. We demonstrate the performance of our method on standard benchmarks using StableDiffusion (Rombach et al., 2022) as the prior.

Accepted at the 2nd Workshop on Frontiers in Probabilistic Inference: Sampling Meets Learning, 39th Conference on Neural Information Processing Systems (NeurIPS 2025)