Vision-Language Latent Diffusion Models (LDMs) (Rombach et al., 2022) provide powerful generative priors for inverse problems. However, existing LDM-based inverse solvers typically require a large number of neural function evaluations (NFEs) and backpropagation through large pretrained components, leading to substantial computational costs and, in some cases, degraded reconstruction quality. We propose a unified Euclidean-Wasserstein-2 gradient-flow framework that jointly performs posterior sampling and prompt optimization in the latent space through a single flow that aligns the prior and posterior with the observed data. Combined with few-step latent text-to-image models, this formulation enables low-NFE inference without backpropagation through autoencoders. Experiments across several canonical imaging inverse problems show that our method achieves state-of-the-art performance with significantly reduced computational cost.
@article{arxiv.2605.07907,
title = {Consistency Regularised Gradient Flows for Inverse Problems},
author = {Alessio Spagnoletti and Tim Y. J. Wang and Marcelo Pereyra and O. Deniz Akyildiz},
journal= {arXiv preprint arXiv:2605.07907},
year = {2026}
}