mlsanityData to 14 Oct 2026

Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priors

arXiv 2510.10968 ↗First posted 13 Oct 2025cs.LG stat.MLcited by 5

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

Abstract (arXiv)

Derivative-free Bayesian inversion arises in science and engineering applications, particularly when forward model is costly or infeasible to differentiate through. Existing derivative-free methods collapse the posterior to a point estimate or return severely over-confident uncertainty on high-dimensional, nonlinear problems. We introduce Blade, which produces accurate and well-calibrated posteriors using an ensemble of interacting particles. Blade leverages diffusion models as data-driven priors, and only queries the forward model through forward evaluations (i.e., derivative-free). Theoretically, we show the convergence and stability of Blade under forward model approximation and prior score estimation error. Empirically, on nonlinear fluid dynamics, Blade produces well-calibrated posterior samples that existing derivative-free methods cannot, as measured by CRPS, the spread-skill ratio, and the rank histogram. Its accuracy and calibration improve consistently with more iterations and particles, backed by our convergence and stability analysis and empirical experiments.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 39 of its 72 references that are in the map. First posted on arXiv 13 Oct 2025.

Builds on

39 of 72 references.

Closest ancestors · 13

Same direction, newest first

  1. 2025InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences14 Mar
  2. 2025Split Gibbs Discrete Diffusion Posterior Sampling3 Mar
  3. 2025Inverse Problem Sampling in Latent Space Using Sequential Monte Carlo9 Feb
  4. 2025A Mixture-Based Framework for Guiding Diffusion Models5 Feb
  5. 2024Ensemble Kalman Diffusion Guidance: A Derivative-free Method for Inverse Problems30 Sep
  6. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing1 Jul
  7. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors29 May
  8. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction25 Mar
  9. 2024Solving General Noisy Inverse Problem via Posterior Sampling: A Policy Gradient Viewpoint15 Mar
  10. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency16 Jul
  11. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  12. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models7 May
1 more
  1. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep

Other references · 26

  1. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  2. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,177
  3. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
  4. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  5. 2022Fast Sampling of Diffusion Models with Exponential Integratorcited by 532
  6. 2017Towards Principled Methods for Training Generative Adversarial Networkscited by 464
  7. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptionscited by 445
  8. 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 413
  9. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problemcited by 236
  10. 2023WeatherBench 2: A benchmark for the next generation of data-driven global weather modelscited by 236
  11. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 232
  12. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 227
14 more
  1. 2025A General Framework for Inference-time Scaling and Steering of Diffusion Modelscited by 224
  2. 2022Convergence for score-based generative modeling with polynomial complexitycited by 177
  3. 2015A Complete Recipe for Stochastic Gradient MCMCcited by 146
  4. 2024Symbolic Music Generation with Non-Differentiable Rule Guided Diffusioncited by 54
  5. 2023Provable Probabilistic Imaging using Score-Based Generative Priorscited by 51
  6. 2018Split-and-augmented Gibbs sampler - Application to large-scale inference problemscited by 47
  7. 2023Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inferencecited by 42
  8. 2018Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Taskscited by 37
  9. 2023Generative Plug and Play: Posterior Sampling for Inverse Problemscited by 24
  10. 2024Conditional sampling within generative diffusion modelscited by 19
  11. 2015A regularizing iterative ensemble Kalman method for PDE-constrained inverse problemscited by 14
  12. 2019Tikhonov Regularization Within Ensemble Kalman Inversioncited by 13
  13. 2019Convergence Acceleration of Ensemble Kalman Inversion in Nonlinear Settingscited by 9
  14. 2024Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAIcited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 5.

5 papers.

  1. 2026Beyond Pairwise Preferences: Listwise Reward-Aware Alignment for Diffusion Modelscited by 1
  2. 2026Flow Annealing Posterior Sampling for Function-Space Regression and Inverse Problemscited by 0
  3. 2026Aligning One-Step Generative Models with Reward-Weighted Transport Distillationcited by 0
  4. 2026Direct Intermediate Initialization for Tilted Diffusion Samplerscited by 0
  5. 2026Noise, Denoise, Correct: MCMC Posterior Sampling with Diffusion Priors in Three Stepscited by 0

Similar, not cited

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  1. 2026Beyond Accuracy: Evaluating Posterior Fidelity of Diffusion Inverse Solvers
  2. 2026D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matching
  3. 2026Latent Diffusion Posterior Sampling with Surrogate Likelihood Guidance for PDE Inverse Problems
  4. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach
  5. 2025Unifying and extending Diffusion Models through PDEs for solving Inverse Problems
  6. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors
  7. 2026FAST-DIPS: Adjoint-Free Analytic Steps and Hard-Constrained Likelihood Correction for Diffusion-Prior Inverse Problems
  8. 2025Bayesian Inverse Problems Meet Flow Matching: Efficient and Flexible Inference via Transformers