mlsanityData to 14 Oct 2026

A Gradient Flow Approach to Solving Inverse Problems with Latent Diffusion Models

arXiv 2509.19276 ↗First posted 23 Sep 2025stat.ML cs.LG stat.COcited by 0

On the map: Diffusion models → Inverse problems and image restoration

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 33 of its 47 references that are in the map. First posted on arXiv 23 Sep 2025.

Builds on

33 of 47 references.

Closest ancestors · 10

Same direction, newest first

  1. 2025Kernel Density Steering: Inference-Time Scaling via Mode Seeking for Image Restoration8 Jul
  2. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach4 Jun
  3. 2025LATINO-PRO: LAtent consisTency INverse sOlver with PRompt Optimization16 Mar
  4. 2024Repulsive Latent Score Distillation for Solving Inverse Problems24 Jun
  5. 2024Diffusion Posterior Proximal Sampling for Image Restoration25 Feb
  6. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency16 Jul
  7. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models2 Jul
  8. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  9. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models7 May
  10. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep

Other references · 23

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  3. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  4. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,177
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  6. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  7. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 6,013
  8. 2023Consistency Modelscited by 1,822
  9. 2023ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillationcited by 1,219
  10. 2023One-step Diffusion with Distribution Matching Distillationcited by 1,019
  11. 2024Improved Distribution Matching Distillation for Fast Image Synthesiscited by 684
  12. 2025Mean Flows for One-step Generative Modelingcited by 561
11 more
  1. 2023Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Modelscited by 236
  2. 2023Particle Guidance: non-I.I.D. Diverse Sampling with Diffusion Modelscited by 71
  3. 2024EM Distillation for One-step Diffusion Modelscited by 62
  4. 2023Taming Mode Collapse in Score Distillation for Text-to-3D Generationcited by 36
  5. 2022Particle algorithms for maximum likelihood training of latent variable modelscited by 26
  6. 2023Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernelcited by 25
  7. 2023SteinDreamer: Variance Reduction for Text-to-3D Score Distillation via Stein Identitycited by 23
  8. 2023Momentum Particle Maximum Likelihoodcited by 12
  9. 2024Efficient Prior Calibration From Indirect Datacited by 11
  10. 2024Particle Semi-Implicit Variational Inferencecited by 7
  11. 2025Efficient Deconvolution in Populational Inverse Problemscited by 4

Built on by

Not cited yet.

Similar, not cited

Close in wording, no citation either way

  1. 2026Consistency Regularised Gradient Flows for Inverse Problems
  2. 2024A Survey on Diffusion Models for Inverse Problems
  3. 2023Training-free Linear Image Inverses via Flows
  4. 2025Latent Refinement via Flow Matching for Training-free Linear Inverse Problem Solving
  5. 2024Fast Samplers for Inverse Problems in Iterative Refinement Models
  6. 2025Diffusion models for inverse problems
  7. 2025ReGuidance: A Simple Diffusion Wrapper for Boosting Sample Quality on Hard Inverse Problems
  8. 2025Solving Inverse Problems with FLAIR