Flow Annealing Posterior Sampling unifies stochastic-process regression and PDE inverse problems.
problem Function-space posterior sampling for stochastic processes and inverse problems.
method Flow Annealing Posterior Sampling (FAPS) using pretrained function-space flow-matching priors.
result Coherent posterior samples with accurate uncertainty quantification.
Diffusion models tackle noisy inverse problems with posterior sampling.
problem Efficiently solving general noisy inverse problems.
method Approximation of posterior sampling for diffusion models.
result Diffusion models can handle various noise statistics and nonlinear problems.
In this paper, we develop a general theory of truncated inverse binomial sampling. In this theory, the fixed-size sampling and inverse binomial sampling are accommodated as special cases. In particular, the classical Chernoff-Hoeffding bound is an immediate consequence of the theory. Moreover, we propose a rigorous and…
This study improves uncertainty quantification in seismic inversion.
problem Uncertainty in seismic inversion due to limited data and model diversity.
method Integrates ensemble methods with importance sampling.
result More accurate uncertainty quantification in velocity models.
New method solves linear inverse problems using diffusion models.
problem Linear inverse problems in various domains.
method Posterior sampling with latent diffusion models.
result Provable sample recovery in linear models, outperforming previous methods.
New method uses CNN for seismic inversion uncertainty quantification.
problem Uncertainty quantification in seismic inversion for noisy data.
method Plug-and-Play Stein Variational Gradient Descent (PnP-SVGD) with CNN denoiser.
result High-resolution, trustworthy posterior samples for subsurface structures.
RePS improves diffusion models for solving inverse problems efficiently.
problem Solving inverse problems with incomplete or noisy measurements.
method Restart for Posterior Sampling (RePS) using pre-trained diffusion models.
result RePS achieves faster convergence and superior reconstruction quality.
Corrects bias in random sampling matrices for improved ML methods.
problem Inversion bias in random sampling matrices hampers ML applications.
method Corrects inversion bias for various random sampling methods.
result Establishes local convergence rates for sub-sampled Newton methods.
Improved diffusion sampling for inverse problems with faster and more robust inference.
problem High computational cost and lack of robustness in diffusion posterior sampling.
method Amortized variational inference with explicit likelihood guidance.
result Improved trade-off between inference speed and robustness to unseen degradations.
Study shows sample complexity for logistic regression with normal covariates.
problem Estimating parameters of logistic regression with normal design.
method Analyzes sample complexity in terms of dimension and inverse temperature.
result Shows two change-points in sample complexity curve based on inverse temperature.
Study inverse problems with measure samples, improving estimator calibration and recovery.
problem Inverse problems with unknown potentials observed through measure samples.
method Introduced convex empirical objectives and sharpened Fenchel--Young losses for finite-dimensional potential classes.
result High-probability parameter recovery bounds for inverse entropic unbalanced optimal transport and inverse JKO learning.
New method tackles video inverse problems using image diffusion models.
problem Spatio-temporal degradation in video inverse problems.
method Leverages image diffusion models to treat time dimension as batch dimension, introduces batch-consistent diffusion sampling.
result Achieves state-of-the-art reconstructions for various spatio-temporal degradations.
Efficiently solves inverse problems with diffusion and flow models in just a few steps.
problem Solving inverse problems like super-resolution, inpainting, or deblurring using diffusion or flow models.
method Conditional Conjugate Integrators framework that projects inverse problem dynamics into a more amenable space for sampling.
result Generates high-quality samples in as few as 5 conditional sampling steps, outperforming competing methods.
Paper tackles estimating initial conditions of spatio-temporal processes from sparse data.
problem Estimating initial conditions of spatio-temporal advection-diffusion processes from sparse data.
method Regularized convex optimization problem with Alternating Direction Method of Multipliers.
result Efficient solutions for non-uniform and shifted uniform sampling schemes.
Bayesian method refines surrogate models for accurate full waveform inversion.
problem Complex input/output relations in full waveform inversion make accurate surrogate models difficult.
method Iterative refinement of surrogate models using MCMC samples and progressively expanding frequency bandwidth.
result Highly accurate surrogate model across full bandwidth enables accurate final MCMC inversion.
We present an adversarial active exploration for inverse dynamics model learning, a simple yet effective learning scheme that incentivizes exploration in an environment without any human intervention. Our framework consists of a deep reinforcement learning (DRL) agent and an inverse dynamics model contesting with each …
A new method uses mixture approximations to improve diffusion models for Bayesian inverse problems.
problem Approximating posterior distributions in Bayesian inverse problems with intractable likelihoods.
method Proposes a mixture-based approximation of intermediate posterior distributions and uses Gibbs sampling for practical sampling.
result Validated the approach on image inverse problems and audio source separation, demonstrating improved performance.
This paper sets a lower bound for sample complexity in inverse reinforcement learning.
problem Finding a reward function that generates a desired optimal policy in MDPs.
method Information-theoretic lower bound using geometric construction and Fano's inequality.
result An O(nlogn) sample complexity lower bound for IRL problems. UCoS avoids forward model evaluations in sampling for large-scale linear inverse problems.
problem Efficient sampling from posterior distributions in large-scale linear inverse problems.
method UCoS approach that learns a task-dependent score function offline and uses affine transformations to derive the conditional score.
result UCoS eliminates the need for forward model evaluations during sampling, making it more efficient.
DPMC improves inverse problem solving with MCMC, reducing error in noisy conditions.
problem Inaccurate posterior approximation in inverse problems with high noise levels.
method DPMC uses Annealed MCMC to sample through a series of intermediate distributions, reducing accumulated error.
result DPMC outperforms DPS in various inverse problems, reducing error and evaluations.
Dual-space sampling tackles ill-conditioned inverse problems with Bayesian methods.
problem Bayesian inference in constrained inverse problems with ill-conditioned solutions.
method Dual-space posterior sampling using ADMM and SVGD.
result Well-calibrated uncertainty estimates and posterior contraction with increasing data.
A new algorithm improves posterior sampling for linear inverse problems.
problem Efficiently sampling from posterior distributions in noisy linear inverse problems.
method Proposes \pddim, a DDIM-type sampler that separately samples along singular directions of the measurement operator.
result The method converges to the Bayesian posterior conditioned on the measurements.
New model for simulating and inferring from inverse problems.
problem Bayesian inverse problems in conditional sampling.
method Invertible generative model using triangular normalizing flows.
result Training loss for invertible map proposed.
Improved sampling efficiency for inverse problems using variance-reduced diffusion methods.
problem Efficiently estimating noisy scores in inverse problems.
method Developed a nonparametric self-normalized importance sampling estimator and a state-dependent blending rule.
result Improved sample quality for fixed simulation budgets in synthetic targets and PDE-governed inverse problems.
New framework maximizes perturbed samples for inverse classification with budget constraints.
problem Maximizing perturbed samples for desired classification outcomes under budget constraints.
method Gradient methods, stochastic processes, Lagrangian relaxations, Gumbel trick.
result Stochastic process-based algorithms outperform in different budget settings.
Improved PDMP samplers for multi-modal distributions using tempering.
problem Struggles of PDMP samplers with multi-modal or heavy-tailed distributions.
method Tempering PDMPs by interpolating between a tractable and posterior distribution.
result PDMP samplers can be improved to sample from multi-modal distributions.
With the recent success of deep neural networks in computer vision, it is important to understand the internal working of these networks. What does a given neuron represent? The concepts captured by a neuron may be hard to understand or express in simple terms. The approach we propose in this paper is to characterize t…
Improved diffusion models for inverse problems by integrating data consistency constraints.
problem Errors in earlier steps of diffusion models during posterior sampling.
method Guided Decoupled Posterior Sampling (GDPS) with data consistency constraint.
result GDPS achieves state-of-the-art performance, improving accuracy over existing methods.
Researchers use GANs to infer physics-based inverse problems, quantifying uncertainty and promoting generalizability.
problem Quantifying uncertainty in physics-based inverse problems.
method Trained conditional Wasserstein GANs with U-Net architecture and conditional instance normalization.
result The approach effectively samples from the posterior and promotes generalizability with out-of-distribution samples.
CCDF reduces diffusion sampling steps for inverse problems.
problem Slow sampling from diffusion models in inverse problems.
method Starting from a single forward diffusion step with better initialization, followed by stochastic contraction.
result Significantly reduced sampling steps for state-of-the-art reconstruction.
EiGLasso speeds up sparse Kronecker-sum covariance estimation.
problem Sparse Kronecker-sum inverse covariance estimation challenges in scalability and parameter identification.
method Newton's method combined with eigendecomposition of sample and feature graphs, approximating Hessian for speed.
result Two to three orders-of-magnitude speed-up on simulated and real-world data.
A new diffusion sampling method combines Krylov subspace and diffusion models for faster and more efficient inverse problems.
problem Efficiently solving large-scale inverse problems in high-performance computing.
method Proposes a novel diffusion sampling strategy that integrates Krylov subspace methods with diffusion models.
result Demonstrates significant speedup (80x faster inference time) and improved reconstruction quality on real-world medical imaging problems.
The decremented learning algorithms are required in machine learning, to prune redundant nodes and remove obsolete inline training samples. In this paper, an efficient decremented learning algorithm to prune redundant nodes is deduced from the incremental learning algorithm 1 proposed in [9] for added nodes, and two de…
New sampling method for Heston model reduces complexity.
problem Efficient sampling for Heston model's time integrated variance.
method Series expansion, change of measure, Chebyshev polynomial approximations.
result Strong, efficient sampling scheme established for Heston model.
A novel diffusion method for Bayesian posterior sampling with theoretical guarantees.
problem Efficiently sampling from complex posterior distributions in Bayesian inversion.
method Diffusion-based posterior sampling using Langevin dynamics and PnP framework.
result The method converges even for multi-modal posterior distributions with theoretical error bounds.
A new method uses DMs as priors for imaging problems, offering more accurate reconstructions.
problem Accurate probabilistic imaging for complex inverse problems.
method Markov chain Monte Carlo algorithm using DMs as plug-and-play priors for solving Bayesian inverse problems.
result Offers more accurate reconstructions and posterior estimation compared to existing methods.
A fast method approximates likelihood scores for noisy linear inverse problems.
problem Solving noisy linear inverse problems efficiently.
method Proposes a simple closed-form approximation to the likelihood score for diffusion and flow-based models.
result Significantly faster than baseline methods while maintaining competitive or better reconstruction performances.
A new method for sampling complex posterior distributions in DDMs.
problem Challenging posterior distributions in DDMs.
method Divide-and-Conquer Posterior Sampling (DCPS)
result Significantly reduces approximation error without retraining.
New method improves DMs for solving inverse problems by maximizing conditional mutual information.
problem Efficiently solving noisy linear inverse problems without additional task-specific training.
method Maximizing conditional mutual information between reconstructed signal and measurement.
result Significantly improves the quality of generated images in inverse problems.
We extend diffusion models to function spaces and introduce a new method for sampling from posterior distributions.
problem Sampling from posterior distributions in infinite-dimensional function spaces using diffusion models.
method Infinite-dimensional extension of Doob's h-transform, Supervised Guidance Training for efficient sampling. result We prove that diffusion models can be conditioned to sample from posterior distributions and introduce a simulation-free score matching objective.
Rewriting history improves RL algorithms for solving multiple tasks.
problem Improving sample efficiency in multi-task reinforcement learning.
method Introducing hindsight relabeling as inverse RL to generalize goal-relabeling techniques.
result Relabeling data using inverse RL accelerates learning in multi-task settings.
Paper introduces STSL, a second-order Tweedie sampler for efficient posterior sampling in inverse problems.
problem Computational challenges in sampling from posterior distributions using latent diffusion models.
method Introduces STSL, a novel second-order Tweedie sampler with tractable reverse process.
result STSL achieves 4X and 8X reduction in neural function evaluations compared to state-of-the-art solvers.
A new machine learning method for Bayesian inverse problems in function spaces.
problem Bayesian inverse problems in function spaces with incompatibility of white noise sources.
method One-step generative transport with amortized neural operator and prior-aligned Gaussian random field.
result Generative operator trained on prior samples and noisy observations generates posterior samples efficiently.
DIN framework directly models hydraulic conductivity and uncertainty.
problem Modeling hydraulic conductivity and uncertainty in groundwater flow.
method DIN utilizes DDPM as a prior learner, incorporating observational data through conditional injection mechanisms.
result DIN generates multiple constraint-satisfying realizations and accurate uncertainty quantification.
New method addresses error bounds for PnP-ULA under mismatched models.
problem Error bounds for PnP-ULA under mismatched measurement and prior models.
method Posterior-L2 pseudometric to quantify error bounds.
result Explicit error bound for PnP-ULA under mismatched posterior distribution.
Unified derivation of diffusion models using PDEs for inverse problems.
problem Solving inverse problems in physics-based applications.
method Deriving diffusion models using PDEs for a unified approach.
result Unified derivation and new class of variance preserving models.
RADIS uses deep regression to create efficient importance sampling for model inversion and emulation.
problem Efficiently sampling from posterior distributions for model inversion and emulation.
method RADIS uses a deep architecture of nested importance sampling schemes to construct a non-parametric emulator that mimics the posterior distribution.
result RADIS asymptotically converges to an exact sampler under mild conditions and can be used as a surrogate model.
Bayesian framework for image inversion using regularization by denoising.
problem Image inversion and regularization in imaging tasks.
method Bayesian approach with Langevin-within-split Gibbs sampling.
result Demonstrates the effectiveness of the proposed method through numerical experiments.