A Gradient Flow Approach to Solving Inverse Problems with Latent Diffusion Models
stat.ML, cs.LG, stat.CO
Submitted: 2025-09-23
Updated: 2026-09-16
Comments: 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
License: http://creativecommons.org/licenses/by/4.0/
The gist: Solving ill-posed inverse problems requires powerful and flexible priors.
Terminology
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.
Sources
- Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach
- Mean Flows for One-step Generative Modeling
- Kernel Density Steering: Inference-Time Scaling via Mode Seeking for Image Restoration
- { Euclidean, Metric, and Wasserstein } Gradient Flows: an overview
- LATINO-PRO: LAtent consisTency INverse sOlver with PRompt Optimization
- Efficient Deconvolution in Populational Inverse Problems
- SteinDreamer: Variance Reduction for Text-to-3D Score Distillation via Stein Identity
- Improved Distribution Matching Distillation for Fast Image Synthesis
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