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.
@article{arxiv.2509.19276,
title = {A Gradient Flow Approach to Solving Inverse Problems with Latent Diffusion Models},
author = {Tim Y. J. Wang and O. Deniz Akyildiz},
journal= {arXiv preprint arXiv:2509.19276},
year = {2025}
}
Comments
Accepted at the 2nd Workshop on Frontiers in Probabilistic Inference: Sampling Meets Learning, 39th Conference on Neural Information Processing Systems (NeurIPS 2025)