Posterior sampling with a pretrained diffusion prior is governed by a conditional score whose intermediate likelihood component is generally intractable. We begin from an ideal one-parameter posterior SDE family in which a stochasticity parameter controls probability-flow transport and stochastic exploration without changing the posterior marginals. To obtain a tractable model, we express the likelihood in a rescaled clean-image coordinate and use log-SNR to organize the resulting posterior proxies. Projecting the diffusion uncertainty through the forward operator then yields a noise-conditioned covariance path whose targets approach the clean posterior. Because endpoint consistency of these targets does not ensure that a surrogate transport follows them, we interleave the transport with a frozen-target Langevin corrector, producing a continuous surrogate SDE. We discretize this model with an outer Lie--Trotter splitting and a variance-matched split-step IMEX predictor that treats the learned prior explicitly, the linear likelihood implicitly, and the stochastic innovation after the implicit solve. We prove marginal invariance of the ideal family, posterior convergence of the continuous surrogate under mixing and transport-defect conditions, and a first-order weak error bound for the discrete algorithm. Experiments on FFHQ and ImageNet with 100 score evaluations demonstrate competitive reconstruction fidelity for super-resolution and deblurring. A controlled 100-image ablation separates scale consistency from the finite-step effects of stochastic-increment placement, continuation, and corrector allocation. A separate noiseless box-inpainting study shows that large exploration reaches a performance plateau only when the matched innovation is injected after the stiff likelihood solve.
Sampling from high-dimensional posterior distributions is a central challenge in Bayesian inference and noisy inverse problems. Standard first-order Langevin-based methods often suffer from slow convergence and sensitivity to step-size hyperparameters, particularly in annealed score-based inverse imaging pipelines. We propose Adaptive Momentum Langevin Dynamics (AMLD), a practical stochastic correction kernel that introduces a momentum variable into the annealed posterior sampling framework and equips it with an annealing-aware momentum retention schedule. The method is fully compatible with the SNIPS framework and retains its coordinate-wise adaptive step structure, acting as a lightweight drop-in replacement for the conventional first-order Langevin correction step. Extensive experiments on three representative image inverse problems—Gaussian deblurring, inpainting, and 4× super-resolution—demonstrate that AMLD consistently achieves strong PSNR and LPIPS performance, with competitive FID in most settings, compared to three state-of-the-art baselines (DDRM, DPS, SNIPS) under both nearly noiseless and noisy measurement conditions, while reaching target reconstruction quality using fewer sampling iterations. The proposed momentum-based sampler provides empirically improved exploration and robustness across evolving posterior landscapes, offering a practical and computationally efficient alternative to first-order annealed Langevin samplers in high-dimensional Bayesian inverse problems.
Bayesian imaging inverse problems often require sampling from high-dimensional posterior distributions. While recent score-based and diffusion models provide expressive Bayesian priors, their sampling procedures remain inherently sequential and computationally expensive for large-scale imaging applications. We propose PiX-MC, a time-parallel posterior sampling framework based on proximal Langevin dynamics and Picard iteration. The proximal-likelihood formulation exploits the fact that many imaging likelihoods admit efficient, problem-specific proximal operators, while Picard refinement exposes parallelism across discretization nodes and naturally supports multi-GPU implementation. To further improve practical scalability and sampling performance, we develop multi-block and annealed variants of the proposed framework. We establish convergence guarantees under transparent assumptions, accommodating non-log-concave posteriors, imperfect learned score models, multi-block implementations, and annealing schedules. Experiments on a diverse collection of imaging inverse problems demonstrate that PiX-MC substantially reduces wall-clock time while preserving reconstruction quality. On a $512\times512\times80$ sparse-view computed tomography (CT) problem, annealed multi-block PiX-MC achieves up to a $50\times$ runtime speedup over the standard Langevin sampler using eight GPUs.
Deliang Wei, Evan Bell, Wenhan Guo et al.· 0 citations
Observation Operator Diffusion is proposed, a unified framework that aligns both the supervision trajectory and feature refinement with the intrinsic recovery order of image structures and introduces GL-CoDA, a decoder that injects scale-specific Gaussian-Lanczos observations across decoding stages for coarse-to-fine feature refinement.
Shaojie Guo, Li-Chen Ma, Haoyang Tong et al.· 0 citations
Pretrained score-based diffusion models provide strong unconditional priors, yet enforcing measurement or physics consistency in inverse problems is often handled by heuristic guidance, intermittent projections, or task-specific conditional training, with limited guarantees of feasibility at the end of inference. We propose terminal-conditioned inversion for score-based SDE priors. Given a frozen Score-SDE prior and a task-defined terminal feasibility specification, we construct an associated backward stochastic differential equation whose adapted solution defines a principled inverse map from the terminal requirement to a prior state at a chosen noise level. Under standard regularity conditions, we establish existence and uniqueness of the adapted solution and obtain terminal consistency by construction. We further develop a practical neural BSDE solver that composes arbitrary pretrained diffusion priors with domain constraints without modifying the score-defined coefficients, producing an anchored prior state that enables neighborhood sampling for uncertainty characterization. Experiments on toy datasets validate stable terminal-conditioned inversion and distributionally consistent neighborhood sampling. As a real-world case study, we apply the framework to sparse-view CT reconstruction and achieve improved reconstruction quality over representative training-free baselines while satisfying strict measurement feasibility under the prescribed terminal specification. Project is available in: \href{https://laplacelab.github.io/BSDEDiffusion/}{https://laplace.center/icmlbsdeI/}
Flow matching has emerged as the state-of-the-art generative model and has been used for plug-and-play (PnP) priors to solve inverse problems in computational imaging. However, existing flow-based inverse solvers assume linear forward models and/or make simplifying approximations in posterior sampling. To circumvent these problems, we introduce FlowSGS, a flow-based posterior sampling method using Split Gibbs Sampling (SGS) to decompose the posterior into a likelihood step and a prior step. Specifically, we sample from the likelihood step using Langevin dynamics and leverage the Stochastic Interpolants (SI) framework to integrate a pretrained flow model into the prior step. We provide a form for the prior step that uses SI's reverse-time SDE, and show connections to previous PnP methods. Moreover, with the aid of the flow prior's straight probability paths and a novel timestep correction technique for the reverse-time SDE, FlowSGS requires fewer network evaluations in its prior step than plug-and-play diffusion samplers. Our experiments show state-of-the-art performance on a range of inverse problems. For the first time, we provide an experiment on a nonlinear inverse problem (Fourier phase retrieval) for flow-based inverse solvers.
Tianao Li, Xin-Hui Qian, Emma Alexander· 0 citations
This work introduces Generative Translation Priors--a Bayesian framework that transforms diffusion-based image-to-image translation models into cross-modality image priors for ill-posed imaging inverse problems, and derives two discretized GTP algorithms based on gradient and proximal likelihood guidance.
Evan Bell, Jiaming Liu, Yifan Chen et al.· 0 citations
Adaptive AI agents can help make BIM data more machine-readable by navigating IFC models, interpreting inconsistent information, and mapping it to defined standards. In this blog, Alok Rawat shares findings from a real-world pilot in construction workflows. The post Adaptive AI Agents in Construction Workflows appeared first on GPT-Lab.
What does it take to trust AI-driven HVAC optimization? Our AI Model Factory combines agents, machine learning, reinforcement learning and deterministic checks in a governed workflow designed for messy, real-world building data. The post We built an AI factory for HVAC control appeared first on GPT-Lab.
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
