mlsanityData to 7 Oct 2026

Consistency Regularised Gradient Flows for Inverse Problems

arXiv 2605.07907 ↗First posted 8 May 2026stat.ML cs.CV cs.LGcited by 1

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

Abstract (arXiv)

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.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 60 of its 98 references that are in the map. First posted on arXiv 8 May 2026.

Builds on

60 of 98 references.

Closest ancestors · 17

Same direction, newest first

  1. 2026Sparse Scheduled Diffusion Guidance for Inverse Problems9 Mar
  2. 2026Fast and Robust Likelihood-Guided Diffusion Posterior Sampling with Amortized Variational Inference6 Feb
  3. 2025LVTINO: LAtent Video consisTency INverse sOlver for High Definition Video Restoration1 Oct
  4. 2025Learning few-step posterior samplers by unfolding and distillation of diffusion models3 Jul
  5. 2025LATINO-PRO: LAtent consisTency INverse sOlver with PRompt Optimization16 Mar
  6. 2025Inverse Problem Sampling in Latent Space Using Sequential Monte Carlo9 Feb
  7. 2025SILO: Solving Inverse Problems with Latent Operators20 Jan
  8. 2024Zero-Shot Image Restoration Using Few-Step Guidance of Consistency Models (and Beyond)29 Dec
  9. 2024Variational Diffusion Posterior Sampling with Midpoint Guidance13 Oct
  10. 2024CoSIGN: Few-Step Guidance of ConSIstency Model to Solve General INverse Problems17 Jul
  11. 2024Repulsive Latent Score Distillation for Solving Inverse Problems24 Jun
  12. 2023Prompt-tuning latent diffusion models for inverse problems2 Oct
5 more
  1. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency16 Jul
  2. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models2 Jul
  3. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  4. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models7 May
  5. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep

Other references · 43

  1. 2021Learning Transferable Visual Models From Natural Language Supervisioncited by 33,456
  2. 2021LoRA: Low-Rank Adaptation of Large Language Modelscited by 14,084
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  5. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  6. 2023SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesiscited by 4,290
  7. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  8. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  9. 2025Wan: Open and Advanced Large-Scale Video Generative Modelscited by 2,536
  10. 2023Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasetscited by 2,526
  11. 2022An Image is Worth One Word: Personalizing Text-to-Image Generation using Textual Inversioncited by 2,231
  12. 2023Consistency Modelscited by 1,778
31 more
  1. 2023ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillationcited by 1,207
  2. 2022Null-text Inversion for Editing Real Images using Guided Diffusion Modelscited by 1,168
  3. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  4. 2023One-step Diffusion with Distribution Matching Distillationcited by 978
  5. 2023Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inferencecited by 826
  6. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
  7. 2024Improved Distribution Matching Distillation for Fast Image Synthesiscited by 648
  8. 2025Mean Flows for One-step Generative Modelingcited by 524
  9. 2023Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusioncited by 448
  10. 2021Knowledge Distillation in Iterative Generative Models for Improved Sampling Speedcited by 344
  11. 2023Hard Prompts Made Easy: Gradient-Based Discrete Optimization for Prompt Tuning and Discoverycited by 329
  12. 2023Understanding Diffusion Objectives as the ELBO with Simple Data Augmentationcited by 293
  13. 2016Learning Representations for Automatic Colorizationcited by 251
  14. 2013A General Framework for Updating Belief Distributionscited by 172
  15. 2018Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problemcited by 123
  16. 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency modelscited by 99
  17. 2026Generative Modeling via Driftingcited by 98
  18. 2025How to build a consistency model: Learning flow maps via self-distillationcited by 96
  19. 2024Multistep Distillation of Diffusion Models via Moment Matchingcited by 76
  20. 2024Isambard-AI: a leadership class supercomputer optimised specifically for Artificial Intelligencecited by 59
  21. 2024The Double-Ellipsoid Geometry of CLIPcited by 42
  22. 2023Prompting Hard or Hardly Prompting: Prompt Inversion for Text-to-Image Diffusion Modelscited by 40
  23. 2024The Superposition of Diffusion Models Using the Ito Density Estimatorcited by 36
  24. 2024On Discrete Prompt Optimization for Diffusion Modelscited by 28
  25. 2022Particle algorithms for maximum likelihood training of latent variable modelscited by 26
  26. 2026Rethinking the Design Space of Reinforcement Learning for Diffusion Models: On the Importance of Likelihood Estimation Beyond Loss Designcited by 17
  27. 2024Error bounds for particle gradient descent, and extensions of the log-Sobolev and Talagrand inequalitiescited by 13
  28. 2025Uni-Instruct: One-step Diffusion Model through Unified Diffusion Divergence Instructioncited by 13
  29. 2024Making Better Use of Unlabelled Data in Bayesian Active Learningcited by 10
  30. 2025Directional Textual Inversion for Personalized Text-to-Image Generationcited by 2
  31. 2025Which Way from B to A: The role of embedding geometry in image interpolation for Stable Diffusioncited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Perturb-and-Solve: Efficient Learned-Operator Conditioning for Latent Diffusion Inverse Problemscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025A Gradient Flow Approach to Solving Inverse Problems with Latent Diffusion Models
  2. 2025Solving Inverse Problems with FLAIR
  3. 2025Latent Refinement via Flow Matching for Training-free Linear Inverse Problem Solving
  4. 2023Training-free Linear Image Inverses via Flows
  5. 2024A Survey on Diffusion Models for Inverse Problems
  6. 2024G2D2: Gradient-Guided Discrete Diffusion for Inverse Problem Solving
  7. 2025Align & Invert: Solving Inverse Problems with Diffusion and Flow-based Models via Representation Alignment
  8. 2026Hybrid-Domain Posterior Sampling for Inverse Problems via Latent Flow Matching