New method uses diffusion models for Bayesian inverse problems.
problem Solving Bayesian inverse problems with linear-Gaussian models.
method Decoupled Diffusion Sequential Monte Carlo (DDSMC) method.
result Asymptotically exact solution demonstrated on various data types.
Bayesian Power Steering fine-tunes large diffusion models for domain adaptation.
problem Fine-tuning pre-trained diffusion models for tasks in a smaller probability space.
method Bayesian framework with a novel network structure (Bayesian Power Steering).
result Bayesian Power Steering achieves an FID score of 10.49 on the COCO17 dataset.
Paper uses RL and diffusion models to solve Bayesian inverse problems.
problem Bayesian inverse problems with latent biases.
method Relative Trajectory Balance (RTB) for RL, conditional diffusion models, off-policy backtracking exploration.
result RTB improves diffusion model posteriors for inverse problems.
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.
New method learns diffusion transition density for Bayesian inference.
problem Bayesian inference on diffusions with inaccessible boundaries.
method Neural Galerkin framework to solve FP equation with Dirac mass.
result Approximates likelihood function for efficient posterior sampling.
This work benchmarks diffusion model-based samplers for Bayesian inverse problems.
problem Optimizing diffusion models for uncertainty quantification in Bayesian inverse problems.
method Introduces three benchmark problems and a unified framework for diffusion model-based posterior sampling.
result Provides insights into strengths and limitations of diffusion model-based samplers.
DiEM trains diffusion models from noisy data using EM.
problem Training diffusion models requires clean data, which is often unavailable.
method DiEM uses expectation-maximization algorithm to train diffusion models from incomplete and noisy observations.
result DiEM leads to proper diffusion models suitable for downstream tasks.
New method improves BLL models for complex datasets.
problem Limited expressive capacity of Gaussian priors in BLL models.
method Combines diffusion techniques and implicit priors for variational learning.
result Enhanced predictive accuracy and uncertainty quantification.
DMVI uses diffusion models for efficient probabilistic inference in PPLs.
problem Efficient probabilistic inference in complex probabilistic programming languages.
method DMVI employs diffusion models as variational approximations to the posterior distribution, optimizing a bound on the marginal likelihood.
result DMVI produces more accurate posterior inferences than existing methods in PPLs with similar computational cost and less manual tuning.
Bayesian approach improves rain field reconstruction using CMLs and DMs.
problem Challenges in accurately reconstructing ground-level rainfall from CML path-integrated measurements.
method Bayesian inverse problem with Diffusion Models as priors.
result Improved performance in rainfall estimation compared to existing methods.
Bayesian inference for stochastic differential equations using Wishart diffusions.
problem Inferring stochastic differential equations for regression and dynamical modeling.
method Bayesian non-parametric approach with semi-parametric Wishart processes.
result Modeling diffusion in stochastic differential equations improves performance and avoids overfitting.
Improving Bayesian Optimization via Training-Aware Conditional Diffusion Models
problem Bayesian Optimization
method Bayesian Optimization with Conditional Diffusion Models
result DMS outperforms standard BO baselines
Paper reviews methods for conditional sampling in generative diffusion models.
problem Extending generative diffusion models to sample from conditional distributions.
method Review of existing computational approaches to conditional sampling.
result Highlight key methodologies for constructing conditional generative samplers.
Paper introduces a fast, robust, scalable method for detecting changes in data streams.
problem Detecting changes in data streams efficiently and reliably.
method Bayesian online changepoint detection with provable robustness and scalability.
result The proposed method is more than 10 times faster than previous approaches and provides provable robustness.
GDiff tackles blind denoising with Gibbs sampling and Monte Carlo inference.
problem Blind denoising of signals with unknown noise parameters.
method Gibbs Diffusion (GDiff) method that alternates sampling steps from a conditional diffusion model and a Monte Carlo sampler.
result GDiff achieves blind denoising of natural images and cosmic microwave background data.
Generative model improves sample quality on ImageNet32.
problem Improving sample quality in generative models.
method Iterative Gaussian posterior inference, treating generated sample as unknown variable.
result Improves sample quality on ImageNet32 over BFNs and VDMs.
DDGM generates realistic ECG signals for clinical use.
problem Generating accurate ECG signals from noisy data.
method Bayesian ECG reconstruction using DDGM trained on healthy ECG data.
result DDGM successfully generates realistic ECG signals for clinical applications.
DAPS++ improves diffusion-based image restoration by decoupling prior and likelihood.
problem Decoupling prior and likelihood in diffusion-based inverse problems.
method Introducing DAPS++, which fully decouples diffusion-based initialization from likelihood-driven refinement.
result Achieves high computational efficiency and robust reconstruction performance.
DAPS++ improves diffusion-based image restoration by decoupling prior and likelihood.
problem Decoupling prior and likelihood in diffusion-based inverse problems for better performance.
method Introducing DAPS++, which separates diffusion initialization from likelihood refinement.
result DAPS++ achieves high computational efficiency and robust reconstruction performance.
SGLDiff approximates Bayesian posterior distributions with subsampling error.
problem Approximating Bayesian posterior distributions in large-scale data settings.
method Stochastic Gradient Langevin Diffusion (SGLDiff) with subsampling.
result The Wasserstein distance between the posterior and SGLDiff's limiting distribution is bounded by a fractional power of the mean waiting time.
DiGS improves sampling from multi-modal distributions.
problem Inadequate mixing in MCMC methods for multi-modal distributions.
method Integrates diffusion models and Gibbs sampling to create an auxiliary noisy distribution.
result DiGS exhibits better mixing for multi-modal distributions than state-of-the-art methods.
A new method for Bayesian inference using diffusion models.
problem Bayesian inference in simulator-based models.
method Score-based diffusion models trained with a sequential training procedure.
result Comparable or superior performance compared to existing methods.
New method uses diffusion models to optimize experimental design efficiently.
problem Optimizing experimental design for high-dimensional and complex settings.
method Introduces a pooled posterior distribution and uses diffusion-based samplers for efficient sampling and optimization.
result Extends Bayesian Optimal Experimental Design to practical scenarios.
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.
A new method for sampling from posterior distributions in Bayesian inverse problems.
problem Sampling from posterior distributions in Bayesian inverse problems is challenging due to intractable terms.
method Proposes a novel approach that decomposes the transitions, allowing a trade-off between complexity of guidance term and prior transitions.
result Validated through experiments on various inverse problems, including challenging cases with latent diffusion models as priors.
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.
Weak diffusion priors can still perform well in inverse problems.
problem Using mismatched or low-fidelity diffusion priors in inverse problems.
method Extensive experiments and theoretical analysis combining Bayesian-consistency theory and local-correlation analysis.
result Weak priors succeed when measurements are highly informative, and they fail in other regimes.
Improved NPE with conditional diffusions and summary networks.
problem Approximating complex posterior distributions efficiently and accurately.
method Conditional diffusions coupled with high-capacity summary networks.
result Conditional diffusions offer improved stability, accuracy, and faster training times.
Blade uses diffusion priors to accurately and calibratedly infer complex systems.
problem Derivative-free Bayesian inversion for high-dimensional, nonlinear problems with costly forward models.
method Blade employs an ensemble of interacting particles and diffusion models as priors, querying forward models only through evaluations.
result Blade produces well-calibrated posterior samples that existing methods cannot, improving with more iterations and particles.
NDPs learn to sample from complex function distributions using neural networks and diffusion models.
problem Learning rich distributions over functions with neural networks.
method NDPs use denoising diffusion models and custom attention blocks to incorporate stochastic process properties.
result NDPs can capture functional distributions close to true Bayesian posteriors and outperform neural processes.
New method uses diffusion models to speed up MCMC sampling.
problem Efficiently exploring high-dimensional and multimodal posterior functions.
method Combines Metropolis-Hastings with diffusion models for global sampling.
result Significant reduction in likelihood evaluations for accurate posterior representation.
HyBO optimizes hybrid structures using diffusion kernels.
problem Optimizing complex interactions between discrete and continuous variables.
method HyBO uses diffusion kernels over hybrid spaces with additive kernel formulation.
result HyBO significantly outperforms state-of-the-art methods on real-world benchmarks.
Infinite-dimensional diffusion models tackle generative tasks for complex data.
problem Challenges in applying diffusion models to infinite-dimensional data.
method Directly formulate diffusion-based generative models in infinite dimensions.
result Developed guidelines for designing infinite-dimensional diffusion models.
PriorGuide adapts diffusion models to new priors at test time.
problem Limited applicability of prior distributions in diffusion-based inference.
method PriorGuide uses a guidance approximation to adapt diffusion models to new priors at test time.
result Enhances the versatility of pre-trained inference models by allowing flexible adaptation to new priors.
Paper introduces a Gibbs sampler for Bayesian inversion of ill-posed problems.
problem Bayesian inversion of ill-posed problems with linear transformation and additive noise.
method Gibbs algorithm based on prior diffusion model.
result Gibbs algorithm offers a guarantee of convergence in a specific situation.
CMCD sampler connects transport and variational inference for efficient sampling.
problem Efficient sampling and generative modeling in Bayesian computation.
method Developed a principled framework using divergences on path space, CMCD sampler with adaptive dynamics.
result CMCD sampler outperforms competing approaches across various experiments.
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.
JADAI optimizes design and inference for parameter estimation.
problem Parameter estimation with active optimization of design variables.
method Jointly trains a policy, history network, and inference network to minimize posterior error.
result Achieves superior or competitive performance across benchmarks.
New method reduces over-pessimism in Bayesian control under parameter uncertainty.
problem Over-pessimism in Bayesian control due to misspecified priors.
method Distributionally robust Bayesian control (DRBC) with strong duality and optimization.
result Validated algorithm on synthetic and real data, reducing over-pessimism.
Discretizations of Langevin diffusions provide a powerful method for sampling and Bayesian inference. However, such discretizations require evaluation of the gradient of the potential function. In several real-world scenarios, obtaining gradient evaluations might either be computationally expensive, or simply impossibl…
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.
Adaptive learning of SPDE solutions using score-based diffusion models.
problem Model errors and reduced accuracy in SPDE solutions due to incomplete physical knowledge and environmental variability.
method Score-based diffusion models with recursive Bayesian inference, incorporating simulation data and observational information.
result Accuracy and robustness of the proposed method demonstrated on benchmark SPDEs.
Extends diffusion models to handle exponential family distributions for inverse problems.
problem Intractability of likelihood score for non-Gaussian observations.
method Evidence trick to approximate likelihood score for exponential family distributions.
result Effective Bayesian inference on complex Poisson processes and malaria prevalence prediction.
PAC-Bayesian theory improves text-to-image models by enforcing alignment and generalization.
problem Text-to-image models struggle with complex prompts, misaligning modifiers and neglecting certain elements.
method Proposes a Bayesian approach with custom priors over attention distributions to enforce desirable properties.
result Achieves state-of-the-art results across multiple metrics on standard benchmarks.
Method solves Bayesian inverse problems in function space without assuming log-concavity.
problem Bayesian inverse problems in infinite-dimensional nonlinear settings.
method Score-based diffusion models as a prior, Langevin-type MCMC on function spaces.
result Provable convergence bound for posterior sampling, dependent on score approximation.
The paper addresses the invariance issue in Bayesian neural networks using linearized Laplace approximation.
problem Bayesian neural networks fail to maintain invariance under reparameterization, leading to different posterior densities for identical functions.
method Developed a geometric view of reparameterizations and a Riemannian diffusion process to extend reparameterization invariance to neural network predictive.
result Empirically improved posterior fit through approximate posterior sampling.
Learning in deep models using Bayesian methods has generated significant attention recently. This is largely because of the feasibility of modern Bayesian methods to yield scalable learning and inference, while maintaining a measure of uncertainty in the model parameters. Stochastic gradient MCMC algorithms (SG-MCMC) a…
New MCMC method improves sampling from multimodal distributions.
problem Sampling from multimodal distributions is challenging for classical MCMC methods.
method Interpolating along the diffusion path, preserving mode weights and mixing properties.
result MAD-Path sampler improves global exploration and mode-weight estimation.