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This research introduces a training-free method that utilizes pretrained latent diffusion models to solve ill-posed inverse problems via Wasserstein gradient flow. By formulating posterior sampling as a regularized flow in the model's latent space, the approach effectively leverages existing generative priors without requiring additional fine-tuning. The study validates this technique on standard benchmarks using Stable Diffusion, offering a novel mathematical framework for integrating diffusion models into scientific inference tasks.
A Gradient Flow Approach to Solving Inverse Problems with Latent Diffusion Models
arXiv:2509.19276v2 Announce Type: replace-cross 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.
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.
Accepted 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 $\mathcal{F}[μ]$ and its derivation; the algorithm and reported results are unchanged
Machine Learning (stat.ML); Machine Learning (cs.LG); Computation (stat.CO)
arXiv:2509.19276 [stat.ML]
(or arXiv:2509.19276v2 [stat.ML] for this version)
From: Tim Y. J. Wang [view email] [v1] Tue, 23 Sep 2025 17:41:43 UTC (15,019 KB) [v2] Wed, 16 Sep 2026 10:19:35 UTC (15,020 KB)
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